Mikhail Al'perin, Alexander V. Osipov
Published 2024-01-29, updated 2024-09-02Version 2
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.
Embedding Theorems for function spaces
An equivalent condition for a uniform space to be coverable
Set convergences and uniform convergence of distance functionals on a bornology
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