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Extensions of S-spaces
| 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 |
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| 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. |
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| 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 |
