The work shows closed universal sets exist for nowhere dense sets in Polish spaces, suggesting implications for σ-compact spaces.
We prove that there exists a closed universal set E⊆X×Y for the nowhere dense sets iff the Polish space X is not σ-compact. We construct closed universal sets for the collection of finite sets of size ≤n and of size precisely n. We develop a technique of construction of universal sets similar to the one of Cieślak and Michalski (2018) but using the properties of the Vietoris topology.
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Nowik et al. (2025) studied this question.
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