Gruenhage spaces and their influence on Banach space renorming theory
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916509364781056 |
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| author | Smith, Richard J. |
| author_facet | Smith, Richard J. |
| contents | In a paper from 1987, Gruenhage defined a class of topological spaces that now bear his name, and used it to solve a problem of Talagrand on the existence of dense $G_δ$ metrizable subsets of Gul'ko compact spaces. Gruenhage's paper became highly influential among researchers in renorming theory, a branch of Banach space theory. In this paper we survey Gruenhage and related spaces, and their interactions with renorming theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gruenhage spaces and their influence on Banach space renorming theory Smith, Richard J. Functional Analysis General Topology 46B20, 54D30 (Primary) In a paper from 1987, Gruenhage defined a class of topological spaces that now bear his name, and used it to solve a problem of Talagrand on the existence of dense $G_δ$ metrizable subsets of Gul'ko compact spaces. Gruenhage's paper became highly influential among researchers in renorming theory, a branch of Banach space theory. In this paper we survey Gruenhage and related spaces, and their interactions with renorming theory. |
| title | Gruenhage spaces and their influence on Banach space renorming theory |
| topic | Functional Analysis General Topology 46B20, 54D30 (Primary) |
| url | https://arxiv.org/abs/2412.04401 |