p-Boundedness in paratopological groups
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Titlep-Boundedness in paratopological groups
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. [-]
Bibliographic citationSánchez, I., & Sanchis, M. (2015). p-Boundedness in paratopological groups. Topology and its Applications, 194, 306-316.
Copyright © 2015 Elsevier B.V. All rights reserved.
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