The Smirnov remainders of uniformly locally connected proper metric spaces

The aim of this paper is to investigate relations between uniform local connectedness and the dimension of the Smirnov remainder. In particular, we devote this paper to calculating the dimension of the Smirnov remainder udRn∖Rn of the n-dimensional Euclidean space (Rn,d) with uniform local connectedness. We show that if (R,d) is uniformly locally connected. Moreover, we introduce a new concept of “thin” covering spaces, and we have the following: If an infinite covering space of a compact 2-manifold is “thin”, then .