Approximate resolutions of uniform spaces

In this paper we generalize the notion of approximate resolution to uniform spaces. More precisely, we obtain the category of approximate resolutions and show that it is equivalent to the category of uniform spaces and uniform maps. Furthermore, we extend the approximative shape theory over uniform spaces, and also we show that approximate resolutions can be used in the uniform shape theory. Thus we will be able to use approximate resolutions as a tool to study the category of uniform spaces and uniform maps. Applications to uniform dimension and equiuniformly continuous maps are given.