K~*-metrizable Spaces And Their Applications

摘要

In this paper, we introduce and study a new class of generalized metric spaces, which we call k* -metrizable spaces, and suggest 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 which has a section s : X → M preserving precompact sets in the sense that the image s(K) of any compact set K is contains in X has compact closure in X.