Simultaneous Sequential Compactness
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915682109620224 |
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| author | Resteghini, Sirio Straffelini, Cesare |
| author_facet | Resteghini, Sirio Straffelini, Cesare |
| contents | A set of sequences is said to converge simultaneously if there exists an infinite subset $H$ of the index set $ω$ such that all sequences converge when restricted to $H$. We discuss simultaneous convergence of sequences in the same or in different sequentially compact spaces; we link the results for different spaces to ones for the same space; we show that simultaneous convergence happens for less than $\mathfrak s$ sequences in spaces with weight bounded by $\mathfrak s$ and for less than $\mathfrak h$ sequences in general; we show a slight generalisation of these results in the context of Hausdorff spaces; and finally we investigate their optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous Sequential Compactness Resteghini, Sirio Straffelini, Cesare General Topology Logic 03E17, 54A25 (Primary) 54D10, 54D30, 54D55 (Secondary) A set of sequences is said to converge simultaneously if there exists an infinite subset $H$ of the index set $ω$ such that all sequences converge when restricted to $H$. We discuss simultaneous convergence of sequences in the same or in different sequentially compact spaces; we link the results for different spaces to ones for the same space; we show that simultaneous convergence happens for less than $\mathfrak s$ sequences in spaces with weight bounded by $\mathfrak s$ and for less than $\mathfrak h$ sequences in general; we show a slight generalisation of these results in the context of Hausdorff spaces; and finally we investigate their optimality. |
| title | Simultaneous Sequential Compactness |
| topic | General Topology Logic 03E17, 54A25 (Primary) 54D10, 54D30, 54D55 (Secondary) |
| url | https://arxiv.org/abs/2512.15593 |