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

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