$P_{\lambda}$-sets and skeletal mappings
Volume 131 / 2013
Colloquium Mathematicum 131 (2013), 89-98
MSC: Primary 54G05; Secondary 54C05, 54C10.
DOI: 10.4064/cm131-1-8
Abstract
We prove that if the topology on the set $\operatorname {Seq}$ of all finite sequences of natural numbers is determined by $P_\lambda $-filters and $\lambda \leq \mathfrak {b}$, then $\operatorname {Seq}$ is a $P_\lambda $-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.
