Menger remainders of topological groups


Bella A., TOKGÖZ S., Zdomskyy L.

ARCHIVE FOR MATHEMATICAL LOGIC, vol.55, pp.767-784, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55
  • Publication Date: 2016
  • Doi Number: 10.1007/s00153-016-0493-8
  • Journal Name: ARCHIVE FOR MATHEMATICAL LOGIC
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.767-784
  • Keywords: Remainder, Topological group, Menger space, Hurewicz space, Scheepers space, Ultrafilter, Forcing, COMBINATORICS

Abstract

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 is -compact. Also, the existence of a Scheepers non--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.