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Extensions of S-spaces

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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 one-point 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 S-spaces.
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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 one-point 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): 2013-08-01
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 -- Cauchy-continuous action -- compactification -- completion -- pseudoquotients
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0004881
Restrictions on Access: public 2013-08-15
Host Institution: UCF

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