The $κ$-Fréchet-Urysohn property for $C_p(X)$ is equivalent to Baireness of $B_1(X)$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909613850361856 |
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| author | Osipov, Alexander V. |
| author_facet | Osipov, Alexander V. |
| contents | 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 $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $κ$-Fréchet-Urysohn property for $C_p(X)$ is equivalent to Baireness of $B_1(X)$ Osipov, Alexander V. General Topology 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 $X$. |
| title | The $κ$-Fréchet-Urysohn property for $C_p(X)$ is equivalent to Baireness of $B_1(X)$ |
| topic | General Topology |
| url | https://arxiv.org/abs/2501.06898 |