The $κ$-Fréchet-Urysohn property for $C_p(X)$ is equivalent to Baireness of $B_1(X)$

Alexander V. Osipov

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arXiv · 2501.06898

The $κ$-Fréchet-Urysohn property for $C_p(X)$ is equivalent to Baireness of $B_1(X)$

Alexander V. Osipov

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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 $B_1(X)$ and, hence, the Banakh property for $C_p(X)$ is equivalent to meagerness of $B_1(X)$. Thus, we obtain one characteristic of the Banakh property for $C_p(X)$ through the property of space $X$.

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BibTeX RIS

Alexander V. Osipov. 2025-05-19. The $κ$-Fréchet-Urysohn property for $C_p(X)$ is equivalent to Baireness of $B_1(X)$. https://arxiv.org/abs/2501.06898

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