Strongly ultrametric preserving functions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929319201210368 |
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| author | Dovgoshey, Oleksiy |
| author_facet | Dovgoshey, Oleksiy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strongly ultrametric preserving functions Dovgoshey, Oleksiy General Topology Primary 54E35, Secondary 26A30 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. |
| title | Strongly ultrametric preserving functions |
| topic | General Topology Primary 54E35, Secondary 26A30 |
| url | https://arxiv.org/abs/2401.15922 |