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arXiv · 2302.05388

High dimensional sequential compactness

César Corral·Osvaldo Guzmán·Carlos López-Callejas
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Abstract

We give examples of $n$-sequentially compact spaces that are not $(n+1)$-sequentially compact under several assumptions. We improve results from Kubis and Szeptycki by building such examples from $\mathfrak{b=c}$ and $\diamondsuit(\mathfrak{b})+\mathfrak{d}=\omega_1$. We also introduce a new splitting-like cardinal invariant and then show that the same holds under $\mathfrak{s=b}$.

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César Corral, Osvaldo Guzmán, Carlos López-Callejas. 2023-02-10. High dimensional sequential compactness. https://arxiv.org/abs/2302.05388

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