On quasi-p-bounded subsets

Sanchis, M.; Tamariz-Mascarúa, A.

Colloquium Mathematicae, Tome 79 (1999), p. 175-189 / Harvested from The Polish Digital Mathematics Library

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 × $P_{R K} (p)$ is bounded in X × $P_{R K} (p)$ , if and only if $c l_{β (X \times P_{R K} (p))} (B \times P_{R K} (p)) = c l_{β X} B \times β (ω)$ , where $P_{R K} (p)$ is the set of Rudin-Keisler predecessors of p.

Publié le : 1999-01-01

Zbl 0970.54007

EUDML-ID : urn:eudml:doc:210710

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     author = {M. Sanchis and A. Tamariz-Mascar\'ua},
     title = {On quasi-p-bounded subsets},
     journal = {Colloquium Mathematicae},
     volume = {79},
     year = {1999},
     pages = {175-189},
     zbl = {0970.54007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p175bwm}
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Sanchis, M.; Tamariz-Mascarúa, A. On quasi-p-bounded subsets. Colloquium Mathematicae, Tome 79 (1999) pp. 175-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p175bwm/

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