Current Search: convergence (x)
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 Title
 LATTICEVALUED CONVERGENCE: QUOTIENT MAPS.
 Creator

Boustique, Hatim, Richardson, Gary, University of Central Florida
 Abstract / Description

The introduction of fuzzy sets by Zadeh has created new research directions in many fields of mathematics. Fuzzy set theory was originally restricted to the lattice , but the thrust of more recent research has pertained to general lattices. The present work is primarily focused on the theory of latticevalued convergence spaces; the category of latticevalued convergence spaces has been shown to possess the following desirable categorical properties: topological, cartesianclosed, and...
Show moreThe introduction of fuzzy sets by Zadeh has created new research directions in many fields of mathematics. Fuzzy set theory was originally restricted to the lattice , but the thrust of more recent research has pertained to general lattices. The present work is primarily focused on the theory of latticevalued convergence spaces; the category of latticevalued convergence spaces has been shown to possess the following desirable categorical properties: topological, cartesianclosed, and extensional. Properties of quotient maps between objects in this category are investigated in this work; in particular, one of our principal results shows that quotient maps are productive under arbitrary products. A category of latticevalued interior operators is defined and studied as well. Axioms are given in order for this category to be isomorphic to the category whose objects consist of all the stratified, latticevalued, pretopological convergence spaces. Adding a latticevalued convergence structure to a group leads to the creation of a new category whose objects are called latticevalued convergence groups, and whose morphisms are all the continuous homomorphisms between objects. The latter category is studied and results related to separation properties are obtained. For the special lattice , continuous actions of a convergence semigroup on convergence spaces are investigated; in particular, invariance properties of actions as well as properties of a generalized quotient space are presented.
Show less  Date Issued
 2008
 Identifier
 CFE0002369, ucf:47811
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002369
 Title
 A COMPARATIVE STUDY OF ANT COLONY OPTIMIZATION.
 Creator

Becker, Matthew, Mohapatra, Ram, University of Central Florida
 Abstract / Description

Ant Colony Optimization (ACO) belongs to a class of biologicallymotivated approaches to computing that includes such metaheuristics as artificial neural networks, evolutionary algorithms, and artificial immune systems, among others. Emulating to varying degrees the particular biological phenomena from which their inspiration is drawn, these alternative computational systems have succeeded in finding solutions to complex problems that had heretofore eluded more traditional techniques. Often,...
Show moreAnt Colony Optimization (ACO) belongs to a class of biologicallymotivated approaches to computing that includes such metaheuristics as artificial neural networks, evolutionary algorithms, and artificial immune systems, among others. Emulating to varying degrees the particular biological phenomena from which their inspiration is drawn, these alternative computational systems have succeeded in finding solutions to complex problems that had heretofore eluded more traditional techniques. Often, the resulting algorithm bears little resemblance to its biological progenitor, evolving instead into a mathematical abstraction of a singularly useful quality of the phenomenon. In such cases, these abstract computational models may be termed biological metaphors. Mindful that a fine line separates metaphor from distortion, this paper outlines an attempt to better understand the potential consequences an insufficient understanding of the underlying biological phenomenon may have on its transformation into mathematical metaphor. To that end, the author independently develops a rudimentary ACO, remaining as faithful as possible to the behavioral qualities of an ant colony. Subsequently, the performance of this new ACO is compared with that of a more established ACO in three categories: (1) the hybridization of evolutionary computing and ACO, (2) the efficacy of daemon actions, and (3) theoretical properties and convergence proofs.
Show less  Date Issued
 2006
 Identifier
 CFE0001192, ucf:46844
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0001192
 Title
 IS MIGRANT INTEGRATION POLICY CONVERGING IN EUROPE? A COMPARISON OF EU12 AND EU15 STATES.
 Creator

Zuardo, Steven, Mirilovic, Nikola, University of Central Florida
 Abstract / Description

Immigration issues have dominated the political discourse of liberal democracies around the world in the 21st century. Recent elections in the United States and the Netherlands focused extensively on migrant flows, illegal immigration and migrant integration. Upcoming elections in France seem to be operating within similar parameters. These occurrences underpin a larger critique about the perceived failure of liberal democratic institutions to contend with immigration trends and successfully...
Show moreImmigration issues have dominated the political discourse of liberal democracies around the world in the 21st century. Recent elections in the United States and the Netherlands focused extensively on migrant flows, illegal immigration and migrant integration. Upcoming elections in France seem to be operating within similar parameters. These occurrences underpin a larger critique about the perceived failure of liberal democratic institutions to contend with immigration trends and successfully integrate migrants within their societies. Nowhere has this critique been more prevalent than within the public and political discourse of the European Union, the institution of focus for this paper. As the EU member states struggle to cope with their migrant issues, scholars are increasingly looking to the larger EU governmental structure to anticipate how the region will handle these challenges. Accordingly, much of the scholarly work done on subjects such as integration policy within the EU are mainly focused upon the perceived convergence of policy amongst member states. The intent of this thesis therefore, is to evaluate the validity of claims that migrant integration policy is converging amongst EU member states, and to explain why this may be the case. This was accomplished via a crosscomparison of policy outcome scores, (provided by the Migration Integration Policy Index), over time between EU15 and EU12 states. The convergence of policy in the EU is a topic that has been routinely addressed by scholars, but by examining the potential trends amongst the traditionally ignored EU12 states, this thesis hopes to contribute to the academic discourse by providing a different perspective.
Show less  Date Issued
 2017
 Identifier
 CFH2000215, ucf:45938
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFH2000215
 Title
 CONVERGENCE OF THE MEAN SHIFT ALGORITHM AND ITS GENERALIZATIONS.
 Creator

Hu, Ting, Li, Xin, University of Central Florida
 Abstract / Description

Mean shift is an effective iterative algorithm widely used in image analysis tasks like tracking, image segmentation, smoothing, filtering, edge detection and etc. It iteratively estimates the modes of the probability function of a set of sample data points based in a region. Mean shift was invented in 1975, but it was not widely used until the work by Cheng in 1995. After that, it becomes popular in computer vision. However the convergence, a key character of any iterative algorithm, has...
Show moreMean shift is an effective iterative algorithm widely used in image analysis tasks like tracking, image segmentation, smoothing, filtering, edge detection and etc. It iteratively estimates the modes of the probability function of a set of sample data points based in a region. Mean shift was invented in 1975, but it was not widely used until the work by Cheng in 1995. After that, it becomes popular in computer vision. However the convergence, a key character of any iterative algorithm, has been rigorously proved only very recently, but with strong assumptions. In this thesis, the method of mean shift is introduced systematically first and then the convergence is established under more relaxed assumptions. Finally, generalization of the mean shift method is also given for the estimation of probability density function using generalized multivariate smoothing functions to meet the need for more real life applications.
Show less  Date Issued
 2011
 Identifier
 CFE0004059, ucf:49133
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004059
 Title
 Iteratively Reweighted Least Squares Minimization with Prior Information: A New Approach.
 Creator

Popov, Dmitriy, Li, Xin, Moore, Brian, Mikusinski, Piotr, University of Central Florida
 Abstract / Description

Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard L1minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to...
Show moreIteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard L1minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of simulation results strongly confirming the utility of their approach, they did not rigorously establish the convergence properties of their algorithm. In this paper, we introduce prior information on the support of the sparse domain of the solution into the algorithm of Daubechies et al. We then provide a rigorous proof of the convergence of the resulting algorithm.
Show less  Date Issued
 2011
 Identifier
 CFE0004154, ucf:49082
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004154
 Title
 THE USE OF FILTERS IN TOPOLOGY.
 Creator

Dasser, Abdellatif, Richardson, Gary, University of Central Florida
 Abstract / Description

Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter...
Show moreSequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).
Show less  Date Issued
 2004
 Identifier
 CFE0000202, ucf:46271
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0000202
 Title
 THE ORIGINS OF LACTASE PERSISTENCE AND ONGOING CONVERGENT EVOLUTION.
 Creator

Keller, Beth, McIntyre, Matthew, University of Central Florida
 Abstract / Description

As a primary factor in human evolution, natural selection is an important component of genetic research. Studies of lactase persistence suggest that positive selection has played a powerful role in the adaptation to a lifelong consumption of fresh milk. Using multiple research studies of lactase persistence and suspected corresponding single nucleotide genetic polymorphisms, this study combines data sources to determine whether evidence exists for natural selection of a specific cytosineto...
Show moreAs a primary factor in human evolution, natural selection is an important component of genetic research. Studies of lactase persistence suggest that positive selection has played a powerful role in the adaptation to a lifelong consumption of fresh milk. Using multiple research studies of lactase persistence and suspected corresponding single nucleotide genetic polymorphisms, this study combines data sources to determine whether evidence exists for natural selection of a specific cytosinetothymine genetic mutation located 13,910 base pairs (T13910) upstream from the lactase gene. This polymorphism has potential to be a causal element for lactase persistence, and data suggest that natural selection has played a role in the rising frequency and distribution of this allele, if only in some regions. European and neighboring regions appear to have the highest frequencies with little or no frequency in Asia, Africa and Indonesia; however the presence of lactase persistence in those areas suggests convergent evolution may be occurring on a phenotypic level. To examine this possibility several other identified polymorphisms in the same region as the T13910 will be included in this study.
Show less  Date Issued
 2011
 Identifier
 CFE0003608, ucf:48890
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0003608
 Title
 Nonparametric and Empirical Bayes Estimation Methods.
 Creator

Benhaddou, Rida, Pensky, Marianna, Han, Deguang, Swanson, Jason, Ni, Liqiang, University of Central Florida
 Abstract / Description

In the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet...
Show moreIn the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet series based empirical Bayes estimator constructed in Pensky and Alotaibi (2005). We propose an adaptive version of this estimator using Lepski's method and show that the estimator attains optimal convergence rates. The theory is supplemented by numerous examples. Our study of the functional deconvolution model expands results of Pensky and Sapatinas (2009, 2010, 2011) to the case of estimating an $(r+1)$dimensional function or dependent errors. In both cases, we derive minimax lower bounds for the integrated square risk over a wide set of Besov balls and construct adaptive wavelet estimators that attain those optimal convergence rates. In particular, in the case of estimating a periodic $(r+1)$dimensional function, we show that by choosing Besov balls of mixed smoothness, we can avoid the ''curse of dimensionality'' and, hence, obtain higher than usual convergence rates when $r$ is large. The study of deconvolution of a multivariate function is motivated by seismic inversion which can be reduced to solution of noisy twodimensional convolution equations that allow to draw inference on underground layer structures along the chosen profiles. The common practice in seismology is to recover layer structures separately for each profile and then to combine the derived estimates into a twodimensional function. By studying the twodimensional version of the model, we demonstrate that this strategy usually leads to estimators which are less accurate than the ones obtained as twodimensional functional deconvolutions. Finally, we consider a multichannel deconvolution model with longrange dependent Gaussian errors. We do not limit our consideration to a specific type of longrange dependence, rather we assume that the eigenvalues of the covariance matrix of the errors are bounded above and below. We show that convergence rates of the estimators depend on a balance between the smoothness parameters of the response function, the smoothness of the blurring function, the long memory parameters of the errors, and how the total number of observations is distributed among the channels.
Show less  Date Issued
 2013
 Identifier
 CFE0004814, ucf:49737
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004814
 Title
 Extensions of Sspaces.
 Creator

Losert, Bernd, Richardson, Gary, Mikusinski, Piotr, Dutkay, Dorin, Brennan, Joseph, Marinescu, Dan, University of Central Florida
 Abstract / Description

Given a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y. Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y. We answer the first question for...
Show moreGiven a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y. Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y. We answer the first question for some particular compactifications like the onepoint compactification and the star compactification as well as for the class of regular compactifications. We answer the second question for the class of regular strict completions. Using these results, we give sufficient conditions under which the pseudoquotient of a compactification/completion of a space is the compactification/completion of the pseudoquotient of the given space.
Show less  Date Issued
 2013
 Identifier
 CFE0004881, ucf:49661
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004881
 Title
 CATEGORICAL PROPERTIES OF LATTICEVALUED CONVERGENCE SPACES.
 Creator

Flores, Paul, Richardson, Gary, University of Central Florida
 Abstract / Description

This work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of LatticeValued Convergence Spaces given by Jäger [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L=.Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of...
Show moreThis work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of LatticeValued Convergence Spaces given by Jäger [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L=.Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of Lattice Valued Fuzzy Convergence Spaces defined and studied by Jäger . Our principal category is shown to be a topological universe and contains a subconstruct isomorphic to the category of probabilistic convergence spaces discussed in Kent and Richardson when L=. Fundamental work in latticevalued convergence from the more general perspective of monads can be found in Gähler . Secondly, diagonal axioms are defined in the category whose objects consist of all the lattice valued convergence spaces. When the latter lattice is linearly ordered, a diagonal condition is given which characterizes those objects in the category that are determined by probabilistic convergence spaces which are topological. Certain background information regarding filters, convergence spaces, and diagonal axioms with its dual are given in Chapter 1. Chapter 2 describes Probabilistic Convergence and associated Diagonal axioms. Chapter 3 defines Jäger convergence and proves that Jäger's construct is isomorphic to a bireflective subconstruct of SLCS. Furthermore, connections between the diagonal axioms discussed and those given by Gähler are explored. In Chapter 4, further categorical properties of SLCS are discussed and in particular, it is shown that SLCS is topological, cartesian closed, and extensional. Chapter 5 explores connections between diagonal axioms for objects in the sub construct δ(PCS) and SLCS. Finally, recommendations for further research are provided.
Show less  Date Issued
 2007
 Identifier
 CFE0001715, ucf:47292
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0001715
 Title
 Estimation and clustering in statistical illposed linear inverse problems.
 Creator

Rajapakshage, Rasika, Pensky, Marianna, Swanson, Jason, Zhang, Teng, Bagci, Ulas, Foroosh, Hassan, University of Central Florida
 Abstract / Description

The main focus of the dissertation is estimation and clustering in statistical illposed linear inverse problems. The dissertation deals with a problem of simultaneously estimating a collection of solutions of illposed linear inverse problems from their noisy images under an operator that does not have a bounded inverse, when the solutions are related in a certain way. The dissertation defense consists of three parts. In the first part, the collection consists of measurements of temporal...
Show moreThe main focus of the dissertation is estimation and clustering in statistical illposed linear inverse problems. The dissertation deals with a problem of simultaneously estimating a collection of solutions of illposed linear inverse problems from their noisy images under an operator that does not have a bounded inverse, when the solutions are related in a certain way. The dissertation defense consists of three parts. In the first part, the collection consists of measurements of temporal functions at various spatial locations. In particular, we studythe problem of estimating a threedimensional function based on observations of its noisy Laplace convolution. In the second part, we recover classes of similar curves when the class memberships are unknown. Problems of this kind appear in many areas of application where clustering is carried out at the preprocessing step and then the inverse problem is solved for each of the cluster averages separately. As a result, the errors of the procedures are usually examined for the estimation step only. In both parts, we construct the estimators, study their minimax optimality and evaluate their performance via a limited simulation study. In the third part, we propose a new computational platform to better understand the patterns of RfMRI by taking into account the challenge of inevitable signal fluctuations and interpretthe success of dynamic functional connectivity approaches. Towards this, we revisit an autoregressive and vector autoregressive signal modeling approach for estimating temporal changes of the signal in brain regions. We then generate inverse covariance matrices fromthe generated windows and use a nonparametric statistical approach to select significant features. Finally, we use Lasso to perform classification of the data. The effectiveness of theproposed method is evidenced in the classification of RfMRI scans
Show less  Date Issued
 2019
 Identifier
 CFE0007710, ucf:52450
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007710
 Title
 Managing Effective Collaboration among Law Enforcement, Intelligence Services, and Military Forces in Fight against Terrorism and Organized Crime.
 Creator

Demirhan, Cihan, Kapucu, Naim, Hu, Qian, Feldheim, Mary Ann, Rivera, Fernando, University of Central Florida
 Abstract / Description

The fight against terrorism and organized crime require strong collaboration between public security organizations. Public security networks include several agencies that are not bound to each other with strong hierarchical ties. Because of a lack of the strong hierarchical structure, managing public networks is not similar to managing a single government agency. This study aims to examine the factors influencing network effectiveness in the public security sector. The main research questions...
Show moreThe fight against terrorism and organized crime require strong collaboration between public security organizations. Public security networks include several agencies that are not bound to each other with strong hierarchical ties. Because of a lack of the strong hierarchical structure, managing public networks is not similar to managing a single government agency. This study aims to examine the factors influencing network effectiveness in the public security sector. The main research questions of the study are: Which factors are important for effectiveness in public security networks? What is the role of interorganizational trust among partner agencies? Which kind of leadership style will achieve the highest performance in public security networks? What is the relative importance of goal convergence and organizational culture in network effectiveness? How does the relationship between interorganizational trust, leadership style, goal convergence and organizational culture impact network effectiveness? In order to find these relations, a selfreported survey was sent to 2,095 current and previous Turkish public security network managers. The study found that interorganizational trust and goal convergence have a positive relationship with network effectiveness. Although facilitator leadership is found to be the most common leadership style in Turkish public security networks, it is found as inappropriate to achieve higher network effectiveness. According to the results, the coproducer network leadership is the most convenient leadership style in terms of network effectiveness. While the results of the descriptive statistics confirm that six specific features of organizational culture in public security sector have negative influence on network effectiveness, the hypothesis testing with the covariance structure model only support the negative impact of competition among partner organization. This study contributes to the literature on network effectiveness with particular proposals for the public security managers and practitioners.
Show less  Date Issued
 2014
 Identifier
 CFE0005479, ucf:50350
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005479
 Title
 Digital Dissonance: Horror Cultures in the Age of Convergent Technologies.
 Creator

Powell, Daniel, McDaniel, Rudy, Campbell, James, Brenckle, Martha, Arnzen, Michael, University of Central Florida
 Abstract / Description

The first two decades of the new millennium have witnessed an abundance of change in the areas of textual production, digital communication, and our collective engagement with the Internet. This study explores these changes, which have yielded both positive and negative cultural and developmental outcomes, as products of digital dissonance. Dissonance is characterized by the disruptive consequences inherent in technology's incursion into the print publication cultures of the twentieth century...
Show moreThe first two decades of the new millennium have witnessed an abundance of change in the areas of textual production, digital communication, and our collective engagement with the Internet. This study explores these changes, which have yielded both positive and negative cultural and developmental outcomes, as products of digital dissonance. Dissonance is characterized by the disruptive consequences inherent in technology's incursion into the print publication cultures of the twentieth century, the explosion in socialmedia interaction that is changing the complexion of human contact, and our expanding reliance on the World Wide Web for negotiating commerce, culture, and communication.This study explores digital dissonance through the prism of an emerging literary subgenre called technohorror. Artists working in the area of technohorror are creating works that leverage the qualities of plausibility, mundanity, and surprise to tell important stories about how technology is altering the human experience in the twentyfirst century. This study explores such subjects as paradigmatic changes in textual production methods, dynamic authorial hybridity, digital materiality in folklore studies, posthumanism, transhumanism, cognitive diminution, and physical degeneration as explored in works of technohorror.The work's rhetorical architecture includes elements of both theoretical and qualitative research. This project expands on City University of New York philosophy professor No(&)#235;l Carroll's definition of arthorror in developing a formal explanation of technohorror and then exploring that literary subgenre through the analysis of a series of contemporary texts and industryrelated trends. The study also contains original interviews with active scholars, artists, editors, and librarians in the horror field to gain a variety of perspectives on these complicated subjects.
Show less  Date Issued
 2017
 Identifier
 CFE0006642, ucf:51231
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006642
 Title
 LatticeValued TFilters and Induced Structures.
 Creator

Reid, Frederick, Richardson, Gary, Brennan, Joseph, Han, Deguang, Lang, SheauDong, University of Central Florida
 Abstract / Description

A complete lattice is called a frame provided meets distribute over arbitrary joins. The implication operation in this context plays a central role. Intuitively, it measures the degree to which one element is less than or equal to another. In this setting, a category is defined by equipping each set with a Tconvergence structure which is defined in terms of Tfilters. This category is shown to be topological, strongly Cartesian closed, and extensional. It is well known that the category of...
Show moreA complete lattice is called a frame provided meets distribute over arbitrary joins. The implication operation in this context plays a central role. Intuitively, it measures the degree to which one element is less than or equal to another. In this setting, a category is defined by equipping each set with a Tconvergence structure which is defined in terms of Tfilters. This category is shown to be topological, strongly Cartesian closed, and extensional. It is well known that the category of topological spaces and continuous maps is neither Cartesian closed nor extensional.Subcategories of compact and of complete spaces are investigated. It is shown that each Tconvergence space has a compactification with the extension property provided the frame is a Boolean algebra. TCauchy spaces are defined and sufficient conditions for the existence of a completion are given. Tuniform limit spaces are also defined and their completions are given in terms of the TCauchy spaces they induce. Categorical properties of these subcategories are also investigated. Further, for a fixed Tconvergence space, under suitable conditions, it is shown that there exists an order preserving bijection between the set of all strict, regular, Hausdorff compactifications and the set of all totally bounded TCauchy spaces which induce the fixed space.
Show less  Date Issued
 2019
 Identifier
 CFE0007520, ucf:52586
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007520