Continuity of the inverse

TL;DR

This paper introduces the concept of elta-Baire spaces and proves that certain classes of spaces, including paratopological groups, are elta-Baire, leading to the conclusion that such groups are topological.

Contribution

The paper defines elta-Baire spaces and establishes that paratopological groups that are elta-Baire are actually topological groups, expanding understanding of the structure of these spaces.

Findings

elta-Baire spaces include locally pseudocompact, Baire p-spaces, Baire elta-spaces, and products of ech-complete spaces.

Paratopological groups that are elta-Baire are topological groups.

Identifies broad classes of spaces that are elta-Baire.

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 \v{C}ech-complete spaces are $\Delta$-Baire spaces.