P_λ-sets and skeletal mappings

Abstract

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 ≤ b, 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.