Geodesic
A note on operators extending partial ultrametrics
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 515-524.

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We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.
Classification : 54C20, 54E35, 54E40
Keywords: partial ultrametric; extension operator; Assouad dimension 
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Tymchatyn, E. D.; Zarichnyi, M. A note on operators extending partial ultrametrics. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 515-524. http://geodesic.mathdoc.fr/item/CMUC_2005__46_3_a12/