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Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of $K$ -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either $0, 1$ , or $Ω$ (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces with index...

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...

Sums of quasicontinuous functions

Ján Borsík (1993)

Mathematica Bohemica

It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.

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