TY - JOUR

T1 - Embedding theorems for function spaces

AU - Al'perin, Mikhail

AU - Nokhrin, Sergei

AU - Osipov, Alexander V.

N1 - The authors would like to thank the referee for careful reading and valuable comments.

PY - 2023

Y1 - 2023

N2 - 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). © 2023 Elsevier B.V.

AB - 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). © 2023 Elsevier B.V.

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U2 - 10.1016/j.topol.2023.108523

DO - 10.1016/j.topol.2023.108523

M3 - Article

VL - 332

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

M1 - 108523

ER -