This research explores compact ultrametric spaces generated by labeled star graphs, highlighting their characteristics and weak similarities to finite spaces.
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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Dovgoshey et al. (2025) studied this question.
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