On a variation of selective separability: S-separability Article Swipe
D. Rakesh Chandra
,
Nur Alam
,
D. Roy
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2511.04059
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2511.04059
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 $U\in \mathcal F$.
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Metadata
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- preprint
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- http://arxiv.org/abs/2511.04059
- https://arxiv.org/pdf/2511.04059
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- green
- OpenAlex ID
- https://openalex.org/W4416023899
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On a variation of selective separability: S-separabilityWork title
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preprintOpenAlex work type
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2025Year of publication
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2025-11-06Full publication date if available
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D. Rakesh Chandra, Nur Alam, D. RoyList of authors in order
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https://arxiv.org/abs/2511.04059Publisher landing page
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