A functional characterization of the Hurewicz property

TL;DR

This paper provides a functional characterization of the Hurewicz covering property for Tychonoff spaces, linking topological covering properties to properties of function spaces.

Contribution

It introduces a new functional characterization of the Hurewicz property, connecting it to the structure of the space of continuous functions with pointwise convergence.

Findings

Characterization of Hurewicz property via function spaces

Link between covering properties and function space topology

New criteria for Hurewicz property in Tychonoff spaces

Abstract

For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence. We give the functional characterization of the covering property of Hurewicz.