A characterization of the Menger property by means of ultrafilter convergence

TL;DR

This paper explores how ultrafilter convergence can characterize Menger and Rothberger properties, analyzing their behavior especially in product spaces, thus providing new insights into their topological structure.

Contribution

It introduces a novel characterization of Menger and Rothberger properties using ultrafilter convergence and examines their behavior under product operations.

Findings

Ultrafilter convergence characterizes Menger and Rothberger properties.

Behavior of these properties under products is analyzed.

Provides new topological insights into classical covering properties.

Abstract

We characterize various Menger/Rothberger related properties by means of ultrafilter convergence, and discuss their behavior with respect to products.