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Compact ultrametric spaces generated by labeled star graphs

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arxiv 2504.02425 v1 pith:64KI2RLS submitted 2025-04-03 math.GN

Oleksiy Dovgoshey , Omer Cantor , Olga Rovenska This is my paper · ORCID
classification math.GN
keywords spacesultrametricgeneratedlabeledcompactgraphsstarus-spaces
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Let US be the class of all ultrametric spaces generated by labeled star graphs. We prove that compact US-spaces are the completions of totally bounded ultrametric spaces generated by decreasingly labeled rays. We characterize the ultrametric spaces which are weakly similar to finite US-spaces and describe these spaces by certain four-point conditions.

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  1. Hausdorff distance between ultrametric balls

    math.GN 2025-08 conditional novelty 7.0 of 10

    For any ultrametric space, its set of closed balls with the Hausdorff distance inherits discreteness, local finiteness, completeness, compactness, and related properties exactly when the original space has them; separ...

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