Bohr compactification of separable locally convex spaces
It is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group $ \mathbb{R} $ of all real numbers. This is the case for each separable real Banach space. In this expository...
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AIMS Press
2025-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2025060 |
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| author | Sidney A. Morris |
| author_facet | Sidney A. Morris |
| author_sort | Sidney A. Morris |
| collection | DOAJ |
| description | It is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group $ \mathbb{R} $ of all real numbers. This is the case for each separable real Banach space. In this expository research note, we state the results explicitly and provide accessible proofs. |
| format | Article |
| id | doaj-art-5d4e93de6433474c8fb393cb1166ea73 |
| institution | OA Journals |
| issn | 2688-1594 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-5d4e93de6433474c8fb393cb1166ea732025-08-20T02:08:24ZengAIMS PressElectronic Research Archive2688-15942025-03-013331333133610.3934/era.2025060Bohr compactification of separable locally convex spacesSidney A. Morris0Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Victoria 3086, AustraliaIt is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group $ \mathbb{R} $ of all real numbers. This is the case for each separable real Banach space. In this expository research note, we state the results explicitly and provide accessible proofs.https://www.aimspress.com/article/doi/10.3934/era.2025060bohr compactificationabelian topological groupbanach spacepontryagin dualitydual groupseparable locally convex space |
| spellingShingle | Sidney A. Morris Bohr compactification of separable locally convex spaces Electronic Research Archive bohr compactification abelian topological group banach space pontryagin duality dual group separable locally convex space |
| title | Bohr compactification of separable locally convex spaces |
| title_full | Bohr compactification of separable locally convex spaces |
| title_fullStr | Bohr compactification of separable locally convex spaces |
| title_full_unstemmed | Bohr compactification of separable locally convex spaces |
| title_short | Bohr compactification of separable locally convex spaces |
| title_sort | bohr compactification of separable locally convex spaces |
| topic | bohr compactification abelian topological group banach space pontryagin duality dual group separable locally convex space |
| url | https://www.aimspress.com/article/doi/10.3934/era.2025060 |
| work_keys_str_mv | AT sidneyamorris bohrcompactificationofseparablelocallyconvexspaces |