The κ-Fréchet-Urysohn property for C_p(X) is equivalent to Baireness of B₁(X)

2025/01/12 by Osipov, Alexander V.
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2501.06898

Abstract

A topological space X is Baire if the intersection of any sequence of open dense subsets of X is dense in X. We establish that the property (κ) for a Tychonoff space X is equivalent to Baireness of B₁(X) and, hence, the Banakh property for C_p(X) is equivalent to meagerness of B₁(X). Thus, we obtain one characteristic of the Banakh property for C_p(X) through the property of space X.

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