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Licensed Unlicensed Requires Authentication Published by De Gruyter January 13, 2020

On ultrametric-preserving functions

  • Oleksiy Dovgoshey
From the journal Mathematica Slovaca

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 obtained. 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.

MSC 2010: 54E35
  1. Communicated by Tomasz Natkaniec

Acknowledgment

The author wish to express the gratitude to all the referees for a number of valuable corrections and suggestions.

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Received: 2019-02-25
Accepted: 2019-07-01
Published Online: 2020-01-13
Published in Print: 2020-02-25

© 2020 Mathematical Institute Slovak Academy of Sciences

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