A note on the continuity of the inverse in paratopological groups

Li-Hong Xie; Shou Lin

doi:10.1556/sscmath.51.2014.3.1286

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 51: Issue 3

A note on the continuity of the inverse in paratopological groups

Authors:

Li-Hong Xie

Li-Hong Xie Wuyi University School of Mathematics and Computational Science Jiangmen 529020 P. R. China

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Shou Lin

Shou Lin Ningde Normal University Institute of Mathematics Ningde 352100 P. R. China

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Pages:: 326–334

Online Publication Date:: 26 Aug 2014

Publication Date:: 01 Sep 2014

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.51.2014.3.1286

Keywords:: Primary 54H11, 54H13, 54H99; Paratopological groups; topological groups; weakly Hausdorff number; co-locally countably compact paratopological groups; 2-pseudocompact paratopological groups

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The problem when a paratopolgical group (or semitopological group) is a topological group is interesting and important. In this paper, we continue to study this problem. It mainly shows that: (1) Let G be a paratopological group and put τ = ωHs(G); then G is a topological group if G is a P_τ-space; (2) every co-locally countably compact paratopological group G with ωHs(G) ≦ ω is a topological group; (3) every co-locally compact paratopological group is a topological group; (4) each 2-pseudocompact paratopological group G with ωHs(G) ≦ ω is a topological group. These results improve some results in [11, 13].

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Studia Scientiarum Mathematicarum Hungarica

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Studia Scientiarum Mathematicarum Hungarica
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