超度量的值域、compactness和可分性
The range of ultrametrics, compactness, and separability
摘要：
本文描述了紧超度量的值域的序型，证明了一个可超度量化的无限拓扑空间$(X, τ)$是紧的当且仅当对于与拓扑$τ$相容的任意两个超度量，值域序同构.还证明了超度量拓扑是可分的当且仅当与该拓扑相容的超度量至多有可数值域集。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
