Menger remainders of topological groups


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Bella A., TOKGÖZ S., Zdomskyy L.

ARCHIVE FOR MATHEMATICAL LOGIC, cilt.55, ss.767-784, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 55
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00153-016-0493-8
  • Dergi Adı: ARCHIVE FOR MATHEMATICAL LOGIC
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.767-784
  • Anahtar Kelimeler: Remainder, Topological group, Menger space, Hurewicz space, Scheepers space, Ultrafilter, Forcing, COMBINATORICS
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.