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

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

doi:10.1016/j.topol.2005.09.013

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

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

Mathematics Department

University of Nis

Research output: Contribution to journal › Article › peer-review

20 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 language	English
Pages (from-to)	1269-1280
Number of pages	12
Journal	Topology and its Applications
Volume	154
Issue number	7 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.topol.2005.09.013
State	Published - 1 Apr 2007

Keywords

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

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10.1016/j.topol.2005.09.013

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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).",

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T2 - Menger- and Rothberger-bounded groups

AU - Babinkostova, L.

AU - Kočinac, Lj D.R.

AU - Scheepers, M.

PY - 2007/4/1

Y1 - 2007/4/1

N2 - 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).

AB - 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).

KW - Infinite game

KW - Menger-bounded group

KW - o-bounded group

KW - Rothberger-bounded group

KW - Selection principle

UR - https://www.scopus.com/pages/publications/33847768863

U2 - 10.1016/j.topol.2005.09.013

DO - 10.1016/j.topol.2005.09.013

M3 - Article

AN - SCOPUS:33847768863

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VL - 154

SP - 1269

EP - 1280

JO - Topology and its Applications

JF - Topology and its Applications

IS - 7 SPEC. ISS.

ER -

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

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Keywords

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