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Extensions of Sspaces
 Date Issued:
 2013
 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 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.
Title:  Extensions of Sspaces. 
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Name(s): 
Losert, Bernd, Author Richardson, Gary, Committee Chair Mikusinski, Piotr, Committee Member Dutkay, Dorin, Committee Member Brennan, Joseph, Committee Member Marinescu, Dan, Committee Member University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2013  
Publisher:  University of Central Florida  
Language(s):  English  
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 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.  
Identifier:  CFE0004881 (IID), ucf:49661 (fedora)  
Note(s): 
20130801 Ph.D. Sciences, Mathematics Doctoral This record was generated from author submitted information. 

Subject(s):  convergence space  Cauchy space  convergence semigroup  Cauchy semigroup  continuous action  Cauchycontinuous action  compactification  completion  pseudoquotients  
Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0004881  
Restrictions on Access:  public 20130815  
Host Institution:  UCF 