Absolute non-Archimedean polyhedral expansions of ultrauniform spaces

Abstract

This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\mathbf{L}$. Theorems about expansions of complete ultrametric and ultrauniform spaces are proved. Absolute polyhedral expansions and inverse mapping systems of expansions for non-complete spaces are investigated. This article also contains results about a relation of $dim(X)$ and dimensions of polyhedra over $\mathbf{L}$.

39 pages, latex