Dieudonn\'{e} completeness of function spaces

Mikhail Al'perin; Alexander V. Osipov

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arXiv · 2401.15923

Dieudonn\'{e} completeness of function spaces

Mikhail Al'perin·Alexander V. Osipov

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Abstract

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.

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BibTeX RIS

Mikhail Al'perin, Alexander V. Osipov. 2024-01-29. Dieudonn\'{e} completeness of function spaces. https://arxiv.org/abs/2401.15923

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