A space is said to be nearly pseudocompact iff is dense in . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.
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...
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...
It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.
In Dually discrete spaces, Topology Appl. 155 (2008), 1420–1425, Alas et. al. proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In Products of certain dually discrete spaces, Topology Appl. 156 (2009), 2832–2837, Peng proved a number of partial results and left open the question of whether the product of two stationary subsets of is dually discrete. We answer the first question affirmatively and as a consequence also give...
Let be the subspace of consisting of all weak -points. It is not hard to see that is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that is a -pseudocompact space for all .
In this paper, we deal with the product of spaces which are either -spaces or -spaces, for some . These spaces are defined in terms of a two-person infinite game over a topological space. All countably compact spaces are -spaces, and every -space is a -space, for every . We prove that if is a set of spaces whose product is a -space, then there is such that is countably compact for every . As a consequence, is a -space iff is countably compact, and if is a -space, then all...