Comeager hereditary families of compact sets are big

Peter Banáš

Comeager hereditary families of compact sets are big

逻辑 2026-08-13 v1

作者: Peter Banáš

摘要

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.

引用

@article{arxiv.2608.13523,
  title  = {Comeager hereditary families of compact sets are big},
  author = {Peter Banáš},
  journal= {arXiv preprint arXiv:2608.13523},
  year   = {2026}
}