A classification of the uniform coverings

Abstract

A classification of the uniform coverings over a given uniformly locally path-wise connected and semi-one connected space is made, by the set of the classes conjugated by themselves subgroups of the fundamental group of the base. We use some well-known theorems in the topological case, proving that they are available in the category of the uniform spaces. We supply the covering space with a suitable uniformity, very closely connected with the uniformity of the base and use it for our investigations.