Completion of a fractal structure

Abstract

Fractal structures were introduced to characterize non-archimedean quasi-metrization, and there is a strong relationship between these two concepts. In this paper we give a construction of a completion of a fractal structure by using inverse limits of a sequence of partially ordered sets. This completion extents nicely all the structures related with a fractal structure like the induced non-archimedean quasi-metric and, in fact, it is a bicompletion of it.

Keywords: Completion, fractal structure, non-archimedean quasi-metric, quasi-pseudometric