Asplund spaces $C_k(X)$ beyond Banach spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908573420748800 |
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| author | Fabian, Marian Kcakol, Jerzy Leiderman, Arkady |
| author_facet | Fabian, Marian Kcakol, Jerzy Leiderman, Arkady |
| contents | This paper addresses the Asplund property for the space of continuous functions $C_k(X)$ equipped with the compact-open topology, when $X$ is an arbitrary Tychonoff space. Motivated by inconsistent definitions in prior literature extending the Asplund property beyond Banach spaces, we provide a unified and self-contained treatment of core results in this context.
A characterization of the Asplund property for $C_k(X)$ is established, alongside a review of classical results, including the Namioka--Phelps theorem and its implications. All proofs are presented in a self-contained manner and rely on standard techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asplund spaces $C_k(X)$ beyond Banach spaces Fabian, Marian Kcakol, Jerzy Leiderman, Arkady Functional Analysis General Topology Primary: 46E10, Secondary: 54C35, 54G12 This paper addresses the Asplund property for the space of continuous functions $C_k(X)$ equipped with the compact-open topology, when $X$ is an arbitrary Tychonoff space. Motivated by inconsistent definitions in prior literature extending the Asplund property beyond Banach spaces, we provide a unified and self-contained treatment of core results in this context. A characterization of the Asplund property for $C_k(X)$ is established, alongside a review of classical results, including the Namioka--Phelps theorem and its implications. All proofs are presented in a self-contained manner and rely on standard techniques. |
| title | Asplund spaces $C_k(X)$ beyond Banach spaces |
| topic | Functional Analysis General Topology Primary: 46E10, Secondary: 54C35, 54G12 |
| url | https://arxiv.org/abs/2510.01873 |