Strongly ultrametric preserving functions

Oleksiy Dovgoshey

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arXiv · 2401.15922

Strongly ultrametric preserving functions

Oleksiy Dovgoshey

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Abstract

An ultrametric preserving function $f$ is said to be strongly ultrametric preserving if ultrametrics $d$ and $f \circ d$ define the same topology on $X$ for each ultrametric space $(X,d)$. The set of all strongly ultrametric preserving functions is characterized by several distinctive features. In particular, it is shown that an ultrametric preserving $f$ belongs to this set iff $f$ preserves the property to be compact.

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Oleksiy Dovgoshey. 2024-01-29. Strongly ultrametric preserving functions. https://arxiv.org/abs/2401.15922

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