The countable rational Urysohn ultrametric space U is the Fraïssé limit of finite two-sorted ultrametric spaces under distance-carrying embeddings and is dc-universal for countable ultrametric spaces, with its completion universal for separable ones.
Kubi\'s , Fraïssé sequences: category-theoretic approach to universal homogeneous structures , Ann
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Universal homogeneous two-sorted ultrametric spaces
The countable rational Urysohn ultrametric space U is the Fraïssé limit of finite two-sorted ultrametric spaces under distance-carrying embeddings and is dc-universal for countable ultrametric spaces, with its completion universal for separable ones.