Characterization of δ-Hurewicz spaces and spaces of δ-continuous functions

Abstract

This work explores the properties of δ-Hurewicz spaces, providing characterization for union of spaces, subspaces, and products of such spaces, as well as we identify under which conditions δ-continuous functions have as image a δ-Hurewicz space. These results are applied to characterize spaces of δ-Hurewicz functions. Specifically, we establish that the countable product of copies of a topological space X with product topology is δ-Hurewicz for a space X being T₁ and δ-compact and also X is δ-compact under certain hypotheses on the function space C_δ(X,X).