Comeager hereditary families of compact sets are big

Peter Banáš

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arXiv · 2608.13523

Comeager hereditary families of compact sets are big

Peter Banáš

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Abstract

Let $X$ be a Polish space and let $\mathcal K(X)$ be its Vietoris hyperspace. A family $\mathcal I\subseteq\mathcal K(X)$ is hereditary if it is downward closed under inclusion. Matheron and Zelen\'y asked whether every comeager hereditary family in $\mathcal K(X)$ contains a dense hereditary $G_\delta$ subfamily. We give an affirmative answer in ZFC.

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Peter Banáš. 2026-08-13. Comeager hereditary families of compact sets are big. https://arxiv.org/abs/2608.13523

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