关于超度量保持函数
On ultrametric-preserving functions
摘要：
给出了伪度量保持函数和半度量保持函数的特征，给出了伪度量可表示为超度量和超伪度量保持函数的复合的结构性质，给出了超度量保持函数的Pongsriiam-Termwuttipong特征的对偶形式.我们还引入了$k$ -分离函数族的概念，并用它来刻画超度量空间。
英文摘要：
Characterizations of pseudoultrametric-preserving functions and semimetric-preserving functions are found. The structural properties of pseudoultrametrics which can be represented as a composition of an ultrametric and ultrametric-pseudoultrametric-preserving function are found. A dual form of Pongsriiam-Termwuttipong characterization of the ultrametric-preserving functions is described. We also introduce a concept of $k$-separating family of functions and use it to characterize the ultrametric spaces.
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。
