Selective screenability and the Hurewicz property

TL;DR

This paper characterizes the Hurewicz covering property in metrizable spaces through metric properties and explores how a weak form of selective screenability combined with it leads to full selective screenability.

Contribution

It provides a new characterization of the Hurewicz property via metrics and establishes a link between weak and full selective screenability under this property.

Findings

Characterization of Hurewicz property in terms of metrics

Weak selective screenability plus Hurewicz implies selective screenability

New insights into the structure of metrizable spaces

Abstract

We characterize the Hurewicz covering property in metrizable spaces in terms of properties of the metrics of the space. Then we show that a weak version of selective screenability, when combined with the Hurewicz property, implies selective screenability.