On quasi-p-bounded subsets

M. Sanchis¹ ; A. Tamariz-Mascarúa¹

¹

Colloquium Mathematicum, Tome 80 (1999) no. 2, pp. 175-189.

Résumé

The notion of quasi-p-boundedness for p ∈ $ω^*$ is introduced and investigated. We characterize quasi-p-pseudocompact subsets of β(ω) containing ω, and we show that the concepts of RK-compatible ultrafilter and P-point in $ω^*$ can be defined in terms of quasi-p-pseudocompactness. For p ∈ $ω^*$, we prove that a subset B of a space X is quasi-p-bounded in X if and only if B × $P_{RK}(p)$ is bounded in X × $P_{RK}(p)$, if and only if $cl_{β(X × P_{RK}(p))}(B× P_{RK}(p)) = cl_{βX} B × β(ω)$, where $P_{RK}(p)$ is the set of Rudin-Keisler predecessors of p.

Détail

DOI : 10.4064/cm-80-2-175-189

Keywords: free ultrafilter, P-point, (quasi)-p-pseudocompact space, Rudin-Keisler pre-order, p-limit point, (quasi)-p-bounded subset, bounded subset