On -continuous functions
On -embedded sets and extension of mappings
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
On --open sets and a decomposition of almost--continuity.
On -continuous selections of small multifunctions and covering properties
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.
On --open sets.
On -closed sets and some forms of continuity
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 .
On -continuity and strong -continuity.
On -generalized closed sets.
On -precontinuous functions.
On -images of separable metric spaces and a problem of Shou Lin
On -metrizable spaces, their continuous images and products
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...
On --images of metric spaces.
On -closed sets and their topology.
On -resolvable and almost--resolvable spaces
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...
Once more on continuity of maximal monotone mappings
Onto Gelfand maps : appendix
Open and closed mappings and compactification
Open and proper maps between convergence spaces
Open, confluent and related mappings on generalized graphs
Open images of orderable spaces