$k^*$-Metrizable Spaces and their Applications
T. O. Banakh, V. I. Bogachev, A. V. Kolesnikov

TL;DR
This paper introduces $k^*$-metrizable spaces, a new class of generalized metric spaces, and explores their applications in topological algebra, functional analysis, and measure theory.
Contribution
It defines $k^*$-metrizable spaces and investigates their properties and applications across various areas of mathematics.
Findings
$k^*$-metrizable spaces generalize metric spaces.
Applications in topological algebra, functional analysis, measure theory.
Characterization of $k^*$-metrizable spaces via continuous maps with sections.
Abstract
In this paper we introduce and study so-called -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 is -metrizable if is the image of a metrizable space under a continuous map having a section that preserves precompact sets in the sense that the image of any compact set has compact closure in .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fixed Point Theorems Analysis · Advanced Banach Space Theory
