E.D. Tymchatyn, M. Zarichnyi
A note on operators extending partial ultrametrics

Comment.Math.Univ.Carolinae 46,3 (2005) 515-524.

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