Semi-topological properties
Sequences of disjoint open sets
Smulian-Eberlein Spaces
Some applications of minimal open sets.
Some properties of maximal open sets.
Some properties of the remainder of Stone-Čech compactifications
Space of Baire functions. I
Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of -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 , or (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
For a free ultrafilter on , the concepts of strong pseudocompactness, strong -pseudocompactness and pseudo--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 characterize the pseudocompactness of the hyperspace of compact subsets...
Sums of quasicontinuous functions
It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.