English

Embedding Theorems for function spaces

General Topology 2023-04-05 v3 Functional Analysis

Abstract

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)C(X,Y) of all continuous functions from a topological space XX into a uniform space YY with the topology of uniform convergence on a family of subsets of XX and with the (weak) set-open topology. We also investigated the following question: how the topological embedding of the space C(X,Y)C(X,Y) is related to algebraic structures (such as topological groups, topological rings and topological vector spaces) on C(X,Y)C(X,Y).

Keywords

Cite

@article{arxiv.2112.07298,
  title  = {Embedding Theorems for function spaces},
  author = {Mikhail Al'perin and Sergei Nokhrin and Alexander V. Osipov},
  journal= {arXiv preprint arXiv:2112.07298},
  year   = {2023}
}

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29 pages