On the Borel complexity and the complete metrizability of spaces of metrics

2024/03/12 by Katsuhisa Koshino, Koshino, Katsuhisa
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2403.07421

Abstract

Given a metrizable space X, let AM(X) be the space of continuous bounded admissible metrics on X, which is endowed with the sup-metric. In this paper, we shall investigate the Borel complexity and the complete metrizability of AM(X) and show that a separable metrizable space X is σ-compact if and only if AM(X) is completely metrizable.

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