Connected economically metrizable spaces

- 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

Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces

We prove that any metrizable non-compact space has a weaker metrizable nowhere locally compact topology. As a consequence, any metrizable non-compact space has a weaker Hausdorff connected topology. The same is established for any Hausdorff space X with a σ -locally finite base whose weight w(X) is a successor cardinal.  2002 Elsevier Science B.V. All rights reserved. AMS classification: Prima...

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...