Abstract: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.
Keywords: partial ultrametric, extension operator, Assouad dimension
AMS Subject Classification: 54E35, 54C20, 54E40