Menger remainders of topological groups

Angelo Bella, Seçil Tokgöz, Lyubomyr Zdomskyy

Published 2015-04-07Version 1

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it it is $\sigma$-compact. Also, the existence of a Scheepers non-$\sigma$-compact remainder of a topological group follows from CH and yields a $P$-point, and hence is independent of ZFC. We also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel'skii.