Remarks on metrizability

Remarks on Metrizability

In connection with those paragraphs of my paper Applications of the theory of Boolean rings to general topology (Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481) dealing with regular spaces, I have long been curious to know whether certain results proved there could be used to obtain the well known theorem that a separable (Hausdorff) space is metrizable if (and only if) it is regular. Since...

Remarks on microperiodic multifunctions

It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

Resolvable Maps Preserve Complete Metrizability

Let X be a Polish space, Y a separable metrizable space, and f : X → Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

Metrizability of Decomposition Spaces

Remarks on Distance-Balanced Graphs

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.