2021/12/14 by Mikhail Al'perin, Al'perin, Mikhail, Sergei Nokhrin +3
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2112.07298
openalex publication_date 2021/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).