Geodesic
$P_{\lambda}$-sets and skeletal mappings
Aleksander Błaszczyk 1   ; Anna Brzeska 1
1 Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland
Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 89-98 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm131-1-8
Keywords: prove topology set operatorname seq finite sequences natural numbers determined lambda filters lambda leq mathfrak operatorname seq lambda set its ech stone compactification improves results simon juh szyma ski corollary obtain generalization result burke concerning skeletal maps partially answer question his

Aleksander Błaszczyk  1   ; Anna Brzeska  1

1 Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland 
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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

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