Selective screenability in topological groups

TL;DR

This paper investigates the selective screenability property in topological groups, providing characterizations in metrizable cases and conditions for property preservation under products, along with a game-theoretic characterization of certain groups.

Contribution

It offers new characterizations of selective screenability in metrizable topological groups using the Haver property and introduces a game-theoretic approach for groups of countable covering dimension.

Findings

Characterizations of selective screenability via Haver properties.

Conditions for property preservation under products.

Game-theoretic characterization of groups with countable covering dimension.

Abstract

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which the properties are preserved by products. Among metrizable groups we characterize the ones of countable covering dimension by a natural game.