%0 Journal Article
%T $k^*$-Metrizable Spaces and their Applications
%A T. O. Banakh
%A V. I. Bogachev
%A A. V. Kolesnikov
%J Mathematics
%D 2008
%I arXiv
%X 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 $f:M\to X$ having a section $s:X\to M$ that preserves precompact sets in the sense that the image $s(K)$ of any compact set $K\subset X$ has compact closure in $X$.
%U http://arxiv.org/abs/0810.3021v1