C(X) determines X - an inherent theory
One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. The development started back from Tychonoff who first pointed out inevitability o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2023-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/17569 |
| _version_ | 1827972391464075264 |
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| author | Biswajit Mitra Sanjib Das |
| author_facet | Biswajit Mitra Sanjib Das |
| author_sort | Biswajit Mitra |
| collection | DOAJ |
| description | One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. The development started back from Tychonoff who first pointed out inevitability of Tychonoff space in this category of problem. Later S. Banach and M. Stone proved independently with slight variance, that if X is compact Hausdorff space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop an inherent theory of this problem to cover up all the works in the literature introducing a notion so called P-compact spaces. |
| first_indexed | 2024-04-09T19:21:46Z |
| format | Article |
| id | doaj.art-ea7e4ba397ad4e219f876a2c109dd85a |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-09T19:21:46Z |
| publishDate | 2023-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-ea7e4ba397ad4e219f876a2c109dd85a2023-04-05T11:41:08ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472023-04-01241839310.4995/agt.2023.1756916759C(X) determines X - an inherent theoryBiswajit Mitra0https://orcid.org/0000-0002-0244-3521Sanjib Das1The University of BurdwanThe University of BurdwanOne of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. The development started back from Tychonoff who first pointed out inevitability of Tychonoff space in this category of problem. Later S. Banach and M. Stone proved independently with slight variance, that if X is compact Hausdorff space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop an inherent theory of this problem to cover up all the works in the literature introducing a notion so called P-compact spaces.https://polipapers.upv.es/index.php/AGT/article/view/17569nearly realcompactreal maximal idealsrm idealrealcompactp-maximal idealp-compact spacestructure space |
| spellingShingle | Biswajit Mitra Sanjib Das C(X) determines X - an inherent theory Applied General Topology nearly realcompact real maximal ideal srm ideal realcompact p-maximal ideal p-compact space structure space |
| title | C(X) determines X - an inherent theory |
| title_full | C(X) determines X - an inherent theory |
| title_fullStr | C(X) determines X - an inherent theory |
| title_full_unstemmed | C(X) determines X - an inherent theory |
| title_short | C(X) determines X - an inherent theory |
| title_sort | c x determines x an inherent theory |
| topic | nearly realcompact real maximal ideal srm ideal realcompact p-maximal ideal p-compact space structure space |
| url | https://polipapers.upv.es/index.php/AGT/article/view/17569 |
| work_keys_str_mv | AT biswajitmitra cxdeterminesxaninherenttheory AT sanjibdas cxdeterminesxaninherenttheory |