Countably compact paratopological groups

Countably compact paratopological groups

Author Alas, O. T. Google Scholar
Sanchis, M. Google Scholar
Institution Universidade Federal de São Paulo (UNIFESP)
Univ Jaume 1
Abstract By means of the theory of bispaces we show that a countably compact To paratopological group (G, tau) is a topological group if and only if (G, tau V tau(-1)) is omega-bounded (here tau(-1) is the conjugate topology of tau). Our approach is premised on the fact that every paratopological countably compact paratopological group is a Baire space and on the notion of a 2-pseudocompact space. We also prove that every omega-bounded (respectively, topologically periodic) Baire paratopological group admits a weaker Hausdorff group topology. in particular, omega-bounded (respectively, topologically periodic) 2-pseudocompact (so, also countably compact) paratopological groups enjoy this property. Some topological properties turning countably compact topological semigroups into topological groups are presented and some open questions are posed.
Keywords 2-pseudocompact (countably compact) paratopological group
Baire space
saturated paratopological group
topologically periodic paratopological group
topological cancellative semigroup
Language English
Date 2007-05-01
Published in Semigroup Forum. New York: Springer, v. 74, n. 3, p. 423-438, 2007.
ISSN 0037-1912 (Sherpa/Romeo, impact factor)
Publisher Springer
Extent 423-438
Access rights Closed access
Type Article
Web of Science ID WOS:000247067800005

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