On cofree S-spaces and cofree S-flows
Let S-Tych be the category of Tychonoff S-spaces for a topological monoid S. We study the cofree S-spaces and cofree S-flows over topological spaces and we prove that for any topological space X and a topological monoid S, the function space C(S,X) with the compact-open topology and the action s · f...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2012-04-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1632 |
| _version_ | 1818549299155304448 |
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| author | Behnam Khosravi |
| author_facet | Behnam Khosravi |
| author_sort | Behnam Khosravi |
| collection | DOAJ |
| description | Let S-Tych be the category of Tychonoff S-spaces for a topological monoid S. We study the cofree S-spaces and cofree S-flows over topological spaces and we prove that for any topological space X and a topological monoid S, the function space C(S,X) with the compact-open topology and the action s · f = (t → f(st)) is the cofree S-space over X if and only if the compact-open topology is admissible and Tychonoff. Finally we study injective S-spaces and we characterize injective cofree S-spaces, when the compact-open topology is admissible and Tychonoff. As a consequence of this result, we characterize the cofree S-spaces and cofree S-flows, when S is a locally compact topological monoid. |
| first_indexed | 2024-12-12T08:31:33Z |
| format | Article |
| id | doaj.art-625fa38a6d2a44cf9d66aded8cb50ca4 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-12T08:31:33Z |
| publishDate | 2012-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-625fa38a6d2a44cf9d66aded8cb50ca42022-12-22T00:31:05ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472012-04-0113111010.4995/agt.2012.16321334On cofree S-spaces and cofree S-flowsBehnam Khosravi0Institute for Advanced Studies in Basic SciencesLet S-Tych be the category of Tychonoff S-spaces for a topological monoid S. We study the cofree S-spaces and cofree S-flows over topological spaces and we prove that for any topological space X and a topological monoid S, the function space C(S,X) with the compact-open topology and the action s · f = (t → f(st)) is the cofree S-space over X if and only if the compact-open topology is admissible and Tychonoff. Finally we study injective S-spaces and we characterize injective cofree S-spaces, when the compact-open topology is admissible and Tychonoff. As a consequence of this result, we characterize the cofree S-spaces and cofree S-flows, when S is a locally compact topological monoid.http://polipapers.upv.es/index.php/AGT/article/view/1632S-spaceS-flowCofree S-spaceCofree S-flow Compact-open topologyInjective S-space |
| spellingShingle | Behnam Khosravi On cofree S-spaces and cofree S-flows Applied General Topology S-space S-flow Cofree S-space Cofree S-flow Compact-open topology Injective S-space |
| title | On cofree S-spaces and cofree S-flows |
| title_full | On cofree S-spaces and cofree S-flows |
| title_fullStr | On cofree S-spaces and cofree S-flows |
| title_full_unstemmed | On cofree S-spaces and cofree S-flows |
| title_short | On cofree S-spaces and cofree S-flows |
| title_sort | on cofree s spaces and cofree s flows |
| topic | S-space S-flow Cofree S-space Cofree S-flow Compact-open topology Injective S-space |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1632 |
| work_keys_str_mv | AT behnamkhosravi oncofreesspacesandcofreesflows |