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arXiv · 2008.10209

An embedding, an extension, and an interpolation of ultrametrics

Yoshito Ishiki
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Abstract

The notion of the 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.

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Yoshito Ishiki. 2020-08-24. An embedding, an extension, and an interpolation of ultrametrics. https://arxiv.org/abs/2008.10209

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