Baireness of the space of pointwise stabilizing functions of the first Baire class

Baireness of the space of pointwise stabilizing functions of the first Baire class

A topological space X is Baire if the Baire Category Theorem holds for X, i.e., the intersection of any sequence of open dense subsets of X is dense in X. In this paper, we have obtained that the space B1st(X) of pointwise stabilizing Baire-one functions is Baire if the space B1(X) of Baire-one func...

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Veröffentlicht in:Topology and its applications 2025-03, Vol.362, p.109218, Article 109218
1. Verfasser: Osipov, Alexander V.
Format: Artikel
Sprache:eng
Schlagworte:
Baire property
Baire-one function
Function space
Stable Baire class
Stable convergence
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Zusammenfassung:A topological space X is Baire if the Baire Category Theorem holds for X, i.e., the intersection of any sequence of open dense subsets of X is dense in X. In this paper, we have obtained that the space B1st(X) of pointwise stabilizing Baire-one functions is Baire if the space B1(X) of Baire-one functions is so. This answers a question posed recently by T. Banakh and S. Gabriyelyan.
ISSN:0166-8641
DOI:10.1016/j.topol.2025.109218