In this paper we extend the notion of quasinormal convergence via ideals and consider the notion of -quasinormal convergence. We then introduce the notion of space as a topological space in which every sequence of continuous real valued functions pointwise converging to , is also -quasinormally convergent to (has a subsequence which is -quasinormally convergent to ) and make certain observations on those spaces.
A dense-in-itself space is called -discrete if the space of real continuous functions on with its box topology, , is a discrete space. A space is called almost--resolvable provided that is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with -resolvable and almost resolvable spaces. We prove that every almost--resolvable space is -discrete, and that these classes coincide in...
In this paper, we prove the following statements: (1) For any cardinal , there exists a Tychonoff star-Lindelöf space such that . (2) There is a Tychonoff discretely star-Lindelöf space such that does not exist. (3) For any cardinal , there exists a Tychonoff pseudocompact -starcompact space such that .
Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space of this kind the inequality “" holds.
* This work was supported by the CNR while the author was visiting the University of Milan.To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function and of its conjugate...
We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C. Arzelà, Dini and P.S. Alexandroff, as well as their statistical versions studied in [Caserta A., Di Maio G., Kočinac L.D.R., {Statistical convergence in function spaces},. Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.] and [Caserta A., Kočinac L.D.R., {On statistical exhaustiveness}, Appl. Math. Lett....
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...