# On quasi-p-bounded subsets

M. Sanchis; A. Tamariz-Mascarúa

Colloquium Mathematicae (1999)

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

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topSanchis, 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 -

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