On partitions of Ellentuck-large sets

Ryszard Frankiewicz; Sławomir Szczepaniak

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arXiv · 1206.5581

On partitions of Ellentuck-large sets

Ryszard Frankiewicz·Sławomir Szczepaniak

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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 $\mathfrak{F}$ of disjoint relatively meager sets such that $\bigcup\mathfrak{F}'$ has the Baire property (relatively) for every subfamily $\mathfrak{F}'\subseteq\mathfrak{F}$. 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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BibTeX RIS

Ryszard Frankiewicz, Sławomir Szczepaniak. 2014-03-27. On partitions of Ellentuck-large sets. https://arxiv.org/abs/1206.5581

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