Simultaneous Sequential Compactness

Sirio Resteghini; Cesare Straffelini

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arXiv · 2512.15593

Simultaneous Sequential Compactness

Sirio Resteghini·Cesare Straffelini

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Abstract

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.

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BibTeX RIS

Sirio Resteghini, Cesare Straffelini. 2025-12-17. Simultaneous Sequential Compactness. https://arxiv.org/abs/2512.15593

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