Combinatorics of open covers (XI): Menger- and Rothberger-bounded groups

L. Babinkostova, Lj D.R. Kočinac, M. Scheepers

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19 Scopus citations

Abstract

We examine Menger-bounded (=o-bounded) and Rothberger-bounded groups. We give internal characterizations of groups having these properties in all finite powers (Theorems 6 and 7, and Theorem 15). In the metrizable case we also give characterizations in terms of measure-theoretic properties relative to left-invariant metrics (Theorems 12 and 19). Among metrizable σ-totally bounded groups we characterize the Rothberger-bounded groups by the corresponding game (Theorem 22).

Original languageEnglish
Pages (from-to)1269-1280
Number of pages12
JournalTopology and its Applications
Volume154
Issue number7 SPEC. ISS.
DOIs
StatePublished - 1 Apr 2007

Keywords

  • Infinite game
  • Menger-bounded group
  • o-bounded group
  • Rothberger-bounded group
  • Selection principle

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