Kurt Gödel Research Center

2015 seminar talk: Remainders of topological groups and Grigorieff forcing

Talk held by Lyubomyr Zdomskyy (KGRC) at the KGRC seminar on 2015-04-30.

Abstract

We will 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.

This is a joint work with Angelo Bella and Secil Tokgoz.