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On quasi-p-bounded subsets

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Sanchis M., Tamariz-Mascarúa A.

Colloquium Mathematicum

1999

tom 80

nr 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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Sanchis M.

1 Tamariz-Mascarúa A.

1 1999

Wyniki wyszukiwania

On quasi-p-bounded subsets