Article

Completion of a fractal structure

Published in: Quaestiones Mathematicae
Volume 40 , issue 5 , 2017 , pages: 679–695

DOI: 10.2989/16073606.2017.1307285

Author(s): J.F. Gálvez-Rodríguez Department of Mathematics, Spain , M.A. Sánchez-Granero Department of Mathematics, Spain

Keywords: Primary 54D35 , Secondary 54E15 , Primary 54D35 , Secondary 54E15

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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.

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