  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.
