A note on operators extending partial ultrametrics
Edward D. Tymchatyn, Michael M. Zarichnyi (2005)
Commentationes Mathematicae Universitatis Carolinae
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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.