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 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 ). (c) 2023 Elsevier B.V. All rights reserved.