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Keywords:
partial ultrametric; extension operator; Assouad dimension
partial ultrametric; extension operator; Assouad dimension
Summary:
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.
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