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

Katsuhisa Koshino

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arXiv · 2403.07421

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

Katsuhisa Koshino

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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 $\sigma$-compact if and only if $AM(X)$ is completely metrizable.

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Katsuhisa Koshino. 2024-03-12. On the Borel complexity and the complete metrizability of spaces of metrics. https://arxiv.org/abs/2403.07421

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