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Continuity of the inverse in groups

E. A. Reznichenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We define $\Delta$-Baire spaces. If a paratopological group $G$ is $\Delta$-Baire space, then $G$ is a topological group. Locally pseudocompact spaces, Baire $p$-spaces, Baire $\Sigma$-spaces, products of Čech-complete spaces are $\Delta$-Baire spaces.

Key words: paratopological groups, semi-topological groups, continuity of the inverse, Baire spaces, $\Delta$-Baire spaces.

UDC: 515.122.4

Received: 06.09.2021

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2022, 77:4, 199–203

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