On quasi-p-bounded subsets

M. Sanchis; A. Tamariz-Mascarúa

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 2, page 175-189
  • ISSN: 0010-1354

Abstract

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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 R K ( p ) is bounded in X × P R K ( p ) , if and only if c l β ( X × P R K ( p ) ) ( B × P R K ( p ) ) = c l β X B × β ( ω ) , where P R K ( p ) is the set of Rudin-Keisler predecessors of p.

How to cite

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Sanchis, M., and Tamariz-Mascarúa, A.. "On quasi-p-bounded subsets." Colloquium Mathematicae 80.2 (1999): 175-189. <http://eudml.org/doc/210710>.

@article{Sanchis1999,
abstract = {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.},
author = {Sanchis, M., Tamariz-Mascarúa, A.},
journal = {Colloquium Mathematicae},
keywords = {free ultrafilter; P-point; (quasi)-p-pseudocompact space; Rudin-Keisler pre-order; p-limit point; (quasi)-p-bounded subset; bounded subset; bounded set; quasi--bounded subset; quasi--pseudocompact space; Rudin-Keisler preorder; -point; -limit point},
language = {eng},
number = {2},
pages = {175-189},
title = {On quasi-p-bounded subsets},
url = {http://eudml.org/doc/210710},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Sanchis, M.
AU - Tamariz-Mascarúa, A.
TI - On quasi-p-bounded subsets
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 2
SP - 175
EP - 189
AB - 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.
LA - eng
KW - free ultrafilter; P-point; (quasi)-p-pseudocompact space; Rudin-Keisler pre-order; p-limit point; (quasi)-p-bounded subset; bounded subset; bounded set; quasi--bounded subset; quasi--pseudocompact space; Rudin-Keisler preorder; -point; -limit point
UR - http://eudml.org/doc/210710
ER -

References

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