A1 Refereed original research article in a scientific journal
Strongly ultrametric preserving functions
Authors: Dovgoshey Oleksiy
Publisher: Elsevier
Publication year: 2024
Journal: Topology and its Applications
Journal name in source: Topology and its Applications
Article number: 108931
Volume: 351
ISSN: 0166-8641
eISSN: 1879-3207
DOI: https://doi.org/10.1016/j.topol.2024.108931(external)
Web address : https://doi.org/10.1016/j.topol.2024.108931(external)
Self-archived copy’s web address: https://arxiv.org/abs/2401.15922(external)
Preprint address: https://arxiv.org/abs/2401.15922v1(external)
Abstract
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.
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.
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