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

Evgenii Reznichenko

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arXiv · 2203.09389

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

Evgenii Reznichenko

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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.

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Evgenii Reznichenko. 2022-03-17. Classes of Baire spaces defined by semi-neighborhoods of the diagonal. https://arxiv.org/abs/2203.09389

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