Some observations on filters with properties defined by open covers
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of with the Cantor set topology.
Some results on sequentially compact extensions
The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.
Spaces with a locally countable -network.
Special sets of reals and weak forms of normality on Isbell--Mrówka spaces
We recall some classical results relating normality and some natural weakenings of normality in -spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like -sets, -sets and -sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being -separated. This new class fits between -sets and perfectly meager sets. We also discuss conditions for an almost disjoint family being potentially...
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...
Sur quelques points de topologie générale. Théorie des nasses et des tramails