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THE BAIRE PROPERTY IN THE REMAINDERS OF SEMITOPOLOGICAL GROUPS

Part of: Generalities Basic constructions Spaces with richer structures

Published online by Cambridge University Press:  21 January 2013

LI-HONG XIE  and
SHOU LIN
LI-HONG XIE*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610065, PR China
SHOU LIN
Affiliation:
Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, PR China Institute of Mathematics, Ningde Normal University, Ningde 352100, PR China email [email protected]
*
✉[email protected]
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Abstract

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It is proved that every remainder of a nonlocally compact semitopological group $G$ is a Baire space if and only if $G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279], and also gives a positive answer to a question of Lin and Lin [‘About remainders in compactifications of paratopological groups’, ArXiv: 1106.3836v1 [Math. GN] 20 June 2011]. We also show that for a nonlocally compact rectifiable space $G$ every remainder of $G$ is either Baire, or meagre and Lindelöf.

Keywords

semitopological groupsrectifiable spacesremaindersdichotomy theoremsBaire spacesp-spaces

MSC classification

Secondary: 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) 54B05: Subspaces 54E20: Stratifiable spaces, cosmic spaces, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 301 - 308
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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