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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 , 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 * , submitted]. These properties in a space X characterize the pseudocompactness of the hyperspace 𝒦 ( X ) of compact subsets...

Strong sequences, binary families and Esenin-Volpin's theorem

Marian Turzański (1992)

Commentationes Mathematicae Universitatis Carolinae

One of the most important and well known theorem in the class of dyadic spaces is Esenin-Volpin's theorem of weight of dyadic spaces. The aim of this paper is to prove Esenin-Volpin's theorem in general form in class of thick spaces which possesses special subbases.

Strong shape of the Stone-Čech compactification

Sibe Mardešić (1992)

Commentationes Mathematicae Universitatis Carolinae

J. Keesling has shown that for connected spaces X the natural inclusion e : X β X of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

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