Best approximation in uniformity type spaces

Abstract

Let X be a set, and $Gamma$ be a collection of subsets of X × X. The object of this paper, is to define a semi-linear uniform space by assuming certain conditions on $Gamma$. The structure of such spaces turned to be a very rich structure. We define closest elements from a given set to a given element in X. Then we study best approximation in semi-linear uniform spaces.