Embedding Theorems for function spaces

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to the function space $C(X,Y)$ of all continuous functions from a topological space $X$...

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Hauptverfasser: Al'perin, Mikhail, Nokhrin, Sergei, Osipov, Alexander V
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Sprache:eng
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Zusammenfassung:In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to 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 $X$ and with the (weak) set-open topology. We also investigated the following question: how the topological embedding of the space $C(X,Y)$ is related to algebraic structures (such as topological groups, topological rings and topological vector spaces) on $C(X,Y)$.
DOI:10.48550/arxiv.2112.07298