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P λ -sets and skeletal mappings

Aleksander Błaszczyk;  Anna Brzeska — 2013

Colloquium Mathematicae

We prove that if the topology on the set Seq of all finite sequences of natural numbers is determined by P λ -filters and λ ≤ , then Seq is a P λ -set in its Čech-Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.

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