Combinatorics of open covers (XI): Menger- and Rothberger-bounded groups |
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Authors: | L Babinkostova M Scheepers |
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Institution: | a Department of Mathematics, Boise State University, Boise, ID 83725, USA b Institute of Mamthematics, University of Nis, Nis 18000, Serbia |
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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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Keywords: | o-bounded group Menger-bounded group Rothberger-bounded group Selection principle Infinite game |
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