Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658155 | Topology and its Applications | 2015 | 8 Pages |
Abstract
We show that if H is a dense subgroup of a T3T3 semitopological group G such that H is a paratopological group, then G is a paratopological group as well. Also, we prove that a semitopological group G is a topological group provided G is T3T3 and it contains a dense topological subgroup.We show that the functors T3T3 and Reg(G)Reg(G) do not respect dense subgroups of semitopological groups. This answers a problem posed by Mikhail Tkachenko.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Iván Sánchez,