Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658184 | Topology and its Applications | 2015 | 11 Pages |
Abstract
We show that bounded subsets of Ï-admissible paratopological groups are p-bounded for all pâÏâ. In other words, they have a similar behavior to bounded subsets of topological groups. We present several new classes of Ï-admissible paratopological groups. In particular, Hausdorff Ï-balanced paratopological groups with countable Hausdorff number belong to this class. Also, we prove that if G is an Ï-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 Ï-admissible (respectively, locally feebly compact) Hausdorff paratopological groups are studied and some clarifying examples are presented.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Iván Sánchez, Manuel Sanchis,