p-Boundedness in paratopological groups
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http://dx.doi.org/10.1016/j.topol.2015.08.010 |
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Title
p-Boundedness in paratopological groupsDate
2015-10Publisher
ElsevierBibliographic citation
Sánchez, I., & Sanchis, M. (2015). p-Boundedness in paratopological groups. Topology and its Applications, 194, 306-316.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0166864115003491Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
We show that bounded subsets of ω-admissible paratopological groups are p -bounded for all p∈ω⁎p∈ω⁎. In other words, they have a similar behavior to bounded subsets of topological groups. We present several new classes ... [+]
We show that bounded subsets of ω-admissible paratopological groups are p -bounded for all p∈ω⁎p∈ω⁎. In other words, they have a similar behavior to bounded subsets of topological groups. We present several new classes of ω-admissible paratopological groups. In particular, Hausdorff ω-balanced paratopological groups with countable Hausdorff number belong to this class. Also, we prove that if G is an ω-admissible paratopological group then so is every subgroup of G and its semiregularization. We analyze, by means of the case of locally feebly compact paratopological groups, how the fact that the semiregularization of a paratopological group G is a topological group influences the properties of the bounded subsets of G. Some properties of C-compact subsets of ω-admissible (respectively, locally feebly compact) Hausdorff paratopological groups are studied and some clarifying examples are presented. [-]
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Topology and its Applications Volume 194, October 2015Rights
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