A note on compact-like semitopological groups

Authors

  • A. Ravsky Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine https://orcid.org/0000-0003-2542-6959
https://doi.org/10.15330/cmp.11.2.442-452

Keywords:

semitopological group, paratopological group, compact-like semitopological group, compact-like paratopological group, continuity of the inverse, joint continuity, separation axioms, countably compact paratopological group, feebly compact topological group
Published online: 2019-12-31

Abstract

We present a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is provided a semiregular semitopological group G which is not T3. We show that each weakly semiregular compact semitopological group is a topological group. On the other hand, constructed examples of quasiregular T1 compact and T2 sequentially compact quasitopological groups, which are not paratopological groups. Also we prove that a semitopological group (G,τ) is a topological group provided there exists a Hausdorff topology στ on G such that (G,σ) is a precompact topological group and (G,τ) is weakly semiregular or (G,σ) is a feebly compact paratopological group and (G,τ) is T3.

How to Cite
(1)
Ravsky, A. A Note on Compact-Like Semitopological Groups. Carpathian Math. Publ. 2019, 11, 442-452.