Abstract

The notion of ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove ultrametric versions of theorems on metric spaces. In this paper, we provide ultrametric versions of the Arens-Eells isometric embedding theorem of metric spaces, the Hausdorff extension theorem of metrics, the Niemytzki-Tychonoff characterization theorem of the compactness, and the author’s interpolation theorem of metrics and theorems on dense subsets of spaces of metrics.

中文翻译：

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超度量的嵌入，扩展和插值$$ ^ * $$

摘要

超度量的概念可以看作是普通度量的零维模拟，并且有望证明度量空间上定理的超度量形式。在本文中，我们提供度量空间的Arens-Eells等距嵌入定理，度量的Hausdorff扩展定理，紧致性的Niemytzki-Tychonoff刻画定理，以及作者关于度量的密集子集的度量和定理的插值定理的超度量版本。指标空间。