On a variation of selective separability: S-separability
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| Format: | Preprint |
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2025
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| _version_ | 1866909889764261888 |
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| author | Chandra, Debraj Alam, Nur Roy, Dipika |
| author_facet | Chandra, Debraj Alam, Nur Roy, Dipika |
| contents | A space $X$ is M-separable (selectively separable) (Scheepers, 1999; Bella et al., 2009) if for every sequence $(Y_n)$ of dense subspaces of $X$ there exists a sequence $(F_n)$ such that for each $n$ $F_n$ is a finite subset of $Y_n$ and $\cup_{n\in \mathbb{N}} F_n$ is dense in $X$. In this paper, we introduce and study a strengthening of M-separability situated between H- and M-separability, which we call S-separability: for every sequence $(Y_n)$ of dense subspaces of $X$ there exists a sequence $(F_n)$ such that for each $n$ $F_n$ is a finite subset of $Y_n$ and for each finite family $\mathcal F$ of nonempty open sets of $X$ some $n$ satisfies $U\cap F_n\neq\emptyset$ for all $U\in \mathcal F$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a variation of selective separability: S-separability Chandra, Debraj Alam, Nur Roy, Dipika General Topology 54D65, 54C35, 54D20, 54D99 A space $X$ is M-separable (selectively separable) (Scheepers, 1999; Bella et al., 2009) if for every sequence $(Y_n)$ of dense subspaces of $X$ there exists a sequence $(F_n)$ such that for each $n$ $F_n$ is a finite subset of $Y_n$ and $\cup_{n\in \mathbb{N}} F_n$ is dense in $X$. In this paper, we introduce and study a strengthening of M-separability situated between H- and M-separability, which we call S-separability: for every sequence $(Y_n)$ of dense subspaces of $X$ there exists a sequence $(F_n)$ such that for each $n$ $F_n$ is a finite subset of $Y_n$ and for each finite family $\mathcal F$ of nonempty open sets of $X$ some $n$ satisfies $U\cap F_n\neq\emptyset$ for all $U\in \mathcal F$. |
| title | On a variation of selective separability: S-separability |
| topic | General Topology 54D65, 54C35, 54D20, 54D99 |
| url | https://arxiv.org/abs/2511.04059 |