TY - JOUR
T1 - Combinatorics of open covers (XI)
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 - http://www.scopus.com/inward/record.url?scp=33847768863&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2005.09.013
DO - 10.1016/j.topol.2005.09.013
M3 - Article
AN - SCOPUS:33847768863
SN - 0166-8641
VL - 154
SP - 1269
EP - 1280
JO - Topology and its Applications
JF - Topology and its Applications
IS - 7 SPEC. ISS.
ER -