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Strong pseudocompact properties

Salvador García-Ferreira;  Y. F. Ortiz-Castillo — 2014

Commentationes Mathematicae Universitatis Carolinae

For a free ultrafilter p on ℕ , the concepts of strong pseudocompactness, strong p -pseudocompactness and pseudo- ω -boundedness were introduced in [Angoa J., Ortiz-Castillo Y.F., Tamariz-Mascarúa A., Ultrafilters and properties related to compactness, Topology Proc. 43 (2014), 183–200] and [García-Ferreira S., Ortiz-Castillo Y.F., Strong pseudocompact properties of certain subspaces of ℕ * , submitted]. These properties in a space X characterize the pseudocompactness of the hyperspace 𝒦 ( X ) of compact subsets...

The subspace of weak P -points of ℕ *

Salvador García-Ferreira;  Y. F. Ortiz-Castillo — 2015

Commentationes Mathematicae Universitatis Carolinae

Let W be the subspace of ℕ * consisting of all weak P -points. It is not hard to see that W is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that W is a p -pseudocompact space for all p ∈ ℕ * .

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