Strongly ultrametric preserving functions

: Dovgoshey Oleksiy

Publisher: Elsevier

: 2024

: Topology and its Applications

: 108931

: 351

: 0166-8641

: 1879-3207

DOI: https://doi.org/10.1016/j.topol.2024.108931

: https://doi.org/10.1016/j.topol.2024.108931

: https://arxiv.org/abs/2401.15922

: https://arxiv.org/abs/2401.15922v1

An ultrametric preserving function f is said to be strongly ultrametric preserving if ultrametrics d and f∘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.