Dieudonné completeness of function spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914932892631040 |
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| author | Al'perin, Mikhail Osipov, Alexander V. |
| author_facet | Al'perin, Mikhail Osipov, Alexander V. |
| contents | A space is called Dieudonné complete if it is complete relative to the maximal uniform structure compatible with its topology. In this paper, we investigated when the function space $C(X,Y)$ of all continuous functions from a topological space $X$ into a uniform space $Y$ with the topology of uniform convergence on a family of subsets of $X$ is Dieudonné complete. Also we proved a generalization of the Eberlein-Šmulian theorem to the class of Banach spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dieudonné completeness of function spaces Al'perin, Mikhail Osipov, Alexander V. General Topology A space is called Dieudonné complete if it is complete relative to the maximal uniform structure compatible with its topology. In this paper, we investigated when the function space $C(X,Y)$ of all continuous functions from a topological space $X$ into a uniform space $Y$ with the topology of uniform convergence on a family of subsets of $X$ is Dieudonné complete. Also we proved a generalization of the Eberlein-Šmulian theorem to the class of Banach spaces. |
| title | Dieudonné completeness of function spaces |
| topic | General Topology |
| url | https://arxiv.org/abs/2401.15923 |