The range of ultrametrics, compactness, and separability

2021/02/22 by Dovgoshey, Oleksiy, Shcherbak, Volodymir · 1 citation
#FOS: Mathematics #General Topology (math.GN) #Primary 54E35 #Secondary 54E45

paper · doi:10.48550/arxiv.2102.10901

Abstract

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 compatible with this topology ultrametric has at most countable range set.

Cited by

• Hausdorff distance between ultrametric balls

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