Dieudonn\'{e} completeness of function spaces
A space is called Dieudonn\'{e} 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...
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| creator | Al'perin, Mikhail Osipov, Alexander V |
| description | A space is called Dieudonn\'{e} 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 Dieudonn\'{e} complete. Also we
proved a generalization of the Eberlein-\v{S}mulian theorem to the class of
Banach spaces. |
| doi_str_mv | 10.48550/arxiv.2401.15923 |
| format | Article |
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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 Dieudonn\'{e} complete. Also we
proved a generalization of the Eberlein-\v{S}mulian theorem to the class of
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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 Dieudonn\'{e} complete. Also we
proved a generalization of the Eberlein-\v{S}mulian theorem to the class of
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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 Dieudonn\'{e} complete. Also we
proved a generalization of the Eberlein-\v{S}mulian theorem to the class of
Banach spaces.</abstract><doi>10.48550/arxiv.2401.15923</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - General Topology |
| title | Dieudonn\'{e} completeness of function spaces |
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