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.