On quasi-p-bounded subsets

Volume 80 / 1999

M. Sanchis, A. Tamariz-Mascarúa Colloquium Mathematicum 80 (1999), 175-189 DOI: 10.4064/cm-80-2-175-189


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.


  • M. Sanchis
  • A. Tamariz-Mascarúa

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image