An Embedding, An Extension, and An Interpolation of Ultrametrics$$^*$$

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.