Classes of Baire spaces defined by semi-neighborhoods of the diagonal

Abstract

With the help of semi-neighborhoods of the diagonal, classes of Baire spaces are defined: $\Delta$, ${\Delta }_h$ and ${\Delta }_s$ Baire spaces. These classes of spaces are studied with the help of topological games. They are useful in studying continuity in groups: paratopological $\Delta$-Baire groups, quasi-topological ${\Delta }_h$-Baire groups, and semitopological ${\Delta }_s$-Baire groups are topological groups.

arXiv admin note: text overlap with arXiv:2203.02937