A1 Refereed original research article in a scientific journal
Hausdorff distance between ultrametric balls
Authors: Dovgoshey, Oleksiy
Publisher: Springer Nature Switzerland AG
Publication year: 2025
Journal: Journal of Mathematical Sciences
ISSN: 1072-3374
eISSN: 1573-8795
DOI: https://doi.org/10.1007/s10958-025-08125-0
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1007/s10958-025-08125-0
Preprint address: https://arxiv.org/abs/2509.00205
Let (𝑋, 𝑑) be an ultrametric space and let 𝑑𝐻 be the Hausdorff distance on the set B¯ 𝑋 of all closed balls in (𝑋, 𝑑). Some interconnections between the properties of the spaces (𝑋, 𝑑) and (B¯ 𝑋, 𝑑𝐻 ) are described. It is established that the space (B¯ 𝑋, 𝑑𝐻 ) has such properties as discreteness, local finiteness, metrical discreteness, completeness, compactness, local compactness if and only if the space (𝑋, 𝑑) has these properties. Necessary and sufficient conditions for the separability of the space (B¯ 𝑋, 𝑑𝐻 ) are also proved.
Funding information in the publication:
The author was supported by grant 359772 of the Academy of Finland.
