On partitions of Ellentuck-large sets

摘要

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 ￡ of disjoint relatively meager sets such that U￡' has the Baire property (relatively) for every subfamily ￡' (∈) ￡. Some remarks concerning continuous restrictions of functions with domain in the Ellentuck space are made.