Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903927 | Topology and its Applications | 2018 | 22 Pages |
Abstract
In the first part of this note, we give some sufficient conditions under which a paratopological group is topologically isomorphic to a subgroup of a product of strongly metrizable paratopological groups. In the second part of this note, we show that a regular (Hausdorff, T1) semitopological group G admits a homeomorphic embedding as a subgroup into a product of regular (Hausdorff, T1) first-countable semitopological groups which are Ï-spaces if and only if G is locally Ï-good, Ï-balanced, Ir(G)â¤Ï (Hs(G)â¤Ï, Sm(G)â¤Ï) and with the property that for every open neighborhood U of the identity e of G the cover {xU:xâG} has a basic refinement F which is Ï-discrete with respect to a countable family V of open neighborhoods of e. In the last part of this note, we give an internal characterization of projectively Ti second-countable semitopological groups, for i=0,1,2.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Liang-Xue Peng, Ming-Yue Guo,