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arXiv · 1902.08747

On ultrametric-preserving functions

Oleksiy Dovgoshey
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Abstract

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.

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Oleksiy Dovgoshey. 2019-02-23. On ultrametric-preserving functions. https://arxiv.org/abs/1902.08747

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