Continuous extension of functions from countable sets

Abstract

Abstract. We give a characterization of countable discrete subspace A of a topological space X such that there exists a (linear) continuous mapping ϕ : C * p (A) → Cp(X) with ϕ(y)| A = y for every y ∈ C * p (A). Using this characterization we answer two questions of A. Arhangel'skii. Moreover, we introduce the notion of well-covered subset of a topological space and prove that for well-covered functionally closed subset A of a topological space X there exists a linear continuous mapping ϕ : Cp(A) → Cp(X) with ϕ(y)| A = y for every y ∈ Cp(A).