Abstract
Semi-linear uniform space is a new space defined by Tallafha, A and Khalil, R in [3], the authors studied some cases of best approximation in such spaces, and gave some open problems in approximation theory in uniform spaces. Besides they defined a set valued map rho on X x X and asked two questions about the properties of rho. The purpose of this paper is to answer these questions. Besides we shall define another set valued map delta on X x X and give more properties of semi-linear uniform spaces using the maps rho and delta. Also we shall give an example of a semi-linear uniform space which is not metrizable.