$P_{\lambda}$-sets and skeletal mappings

Tom 131 / 2013

Aleksander Błaszczyk, Anna Brzeska Colloquium Mathematicum 131 (2013), 89-98 MSC: Primary 54G05; Secondary 54C05, 54C10. DOI: 10.4064/cm131-1-8

Streszczenie

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.

Autorzy

  • Aleksander BłaszczykInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • Anna BrzeskaInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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