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arXiv · 2503.12571

Critical ideals for compact spaces

Rafał Filipów·Małgorzata Kowalczuk·Adam Kwela
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Abstract

For each countable ordinal $\alpha$, we introduce an ideal $conv_\alpha$ and use it to characterize the class of all compact countable spaces which are homeomorphic to the space $\omega^{\alpha}\cdot n+1$ with the order topology. The characterization is expressed in terms of finding a convergent subsequence defined on a set not belonging to $conv_\alpha$.

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Rafał Filipów, Małgorzata Kowalczuk, Adam Kwela. 2025-03-16. Critical ideals for compact spaces. https://arxiv.org/abs/2503.12571

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