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 $-set in its Čech–Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.
@article{10_4064_cm131_1_8,
author = {Aleksander B{\l}aszczyk and Anna Brzeska},
title = {$P_{\lambda}$-sets and skeletal mappings},
journal = {Colloquium Mathematicum},
pages = {89--98},
year = {2013},
volume = {131},
number = {1},
doi = {10.4064/cm131-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm131-1-8/}
}
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Aleksander Błaszczyk; Anna Brzeska. $P_{\lambda}$-sets and skeletal mappings. Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 89-98. doi: 10.4064/cm131-1-8
