Weak selections and suborderable metrizable spaces

SELECTIONS, k-METRIZABLE COMPACTA, AND SUPEREXTENSIONS

A selection theorem for set-valued maps into spaces with binary normal closed subbases is established. This theorem implies some results of A. Ivanov (see [5], [6]) concerning superextensions of k-metrizable compacta. A characterization of k-metrizable compacta in terms of usco retractions into superextensions and extension of functions is also provided.

- Metrizable Spaces and Their Applications

In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...

Proto-metrizable fuzzy topological spaces

Continuity in Separable Metrizable and Lindelöf Spaces

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto pr...

Continuity in Separable Metrizable and Lindelöf Spaces

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is such a topology precisely when the cardinality of X is no greater than c, the cardinality of the continuum. We go on to...