On partitions of Ellentuck-large sets

2012/06/25 by Ryszard Frankiewicz, Frankiewicz, Ryszard, Sławomir Szczepaniak +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.1206.5581

openalex publication_date 2012/06/25 · arxiv created 2014/03/27 · arxiv updated 2014/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that no non-meager subspace of the space [ω]^ω equipped with the Ellentuck topology does admit a Kuratowski partition, that is such a subset cannot be covered by a family \mathfrakF of disjoint relatively meager sets such that \bigcup\mathfrakF' has the Baire property (relatively) for every subfamily \mathfrakF'⊆\mathfrakF. It is also shown that the existence of Kuratowski partitions is not a metric problem. Some remarks concerning continuous restrictions of functions with domain in the Ellentuck space are made.

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