The spaces for which each -continuous function can be extended to a -small point-open l.s.cṁultifunction (resp. point-closed u.s.cṁultifunction) are studied. Some sufficient conditions and counterexamples are given.
In this paper, we further the study of -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using -open and -open sets. Among other results, it is shown a weakly -retract of a Hausdorff space is a -closed subset of .
A space is said to be -metrizable if it has a -discrete -base. The behavior of -metrizable spaces under certain types of mappings is studied. In particular we characterize strongly -separable spaces as those which are the image of a -metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a -metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a -metrizable topological group must be metrizable receives...
We continue the study of almost--resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost--resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded space with countable tightness and every space with -weight is hereditarily almost--resolvable, (2) every crowded paracompact space which is the closed preimage of a crowded Fréchet space in such a way that the...
For the functor of upper semicontinuous capacities in the category of compact Hausdorff spaces and two of its subfunctors, we prove open mapping theorems. These are counterparts of the open mapping theorem for the probability measure functor proved by Ditor and Eifler.
We show that a (weakly) Whyburn space may be mapped continuously via an open map onto a non (weakly) Whyburn space . This fact may happen even between topological groups and , a homomorphism, Whyburn and not even weakly Whyburn.