The range of ultrametrics, compactness, and separability

We describe the order type of range sets of compact ultrametrics and show that an ultrametrizable infinite topological space (X,τ) is compact iff the range sets are order isomorphic for any two ultrametrics compatible with the topology τ. It is also shown that an ultrametrizable topology is separable iff every ultrametric, compatible with this topology, has at most countable range set.