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 ...

We prove a that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls. We also discuss a connection between this uniformity condition and some results on the dynamics of the geodesic flow for such surfaces. Finally, we give a short proof of topological entropy rigidity f...

Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that each these measures some similar or property. Such combined with metric to yield a which are respect multiple

Abstract In the high-energy physics literature one finds statements such as “matrix algebras converge to sphere”. Earlier I provided a general precise setting for understanding statements, in which matrix are viewed quantum metric spaces, and convergence is with respect Gromov–Hausdorff-type distance. But physicists want even more treat structures on spheres (and other spaces), vector bundles, ...

Generalized Geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. Example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. As an application, existence of coincidencefuzzy p...