Lindelof indestructibility, topological games and selection principles

TL;DR

This paper explores the cardinality bounds of Lindel"of spaces with points ${ m G}_\delta$, using topological games and selection principles like the Rothberger property to extend classical results.

Contribution

It advances understanding of Lindel"of spaces with ${ m G}_\delta$ points by applying infinite games and selection principles to establish new cardinality bounds.

Findings

Established new cardinality bounds for Lindel"of spaces with ${ m G}_\delta$ points.

Demonstrated the effectiveness of topological games in analyzing space cardinalities.

Extended classical results to broader classes of topological spaces.

Abstract

Arhangel'skii proved that if a first countable Hausdorff space is Lindel\"of, then its cardinality is at most $2^{\aleph_0}$. Such a clean upper bound for Lindel\"of spaces in the larger class of spaces whose points are ${\sf G}_{\delta}$ has been more elusive. In this paper we continue the agenda started in F.D. Tall, On the cardinality of Lindel\"of spaces with points $G_{\delta}$, Topology and its Applications 63 (1995), 21 - 38, of considering the cardinality problem for spaces satisfying stronger versions of the Lindel\"of property. Infinite games and selection principles, especially the Rothberger property, are essential tools in our investigations