Uniform spaces

This study focuses on the topologic properties of uniform spaces, within this subject the uniform spaces are examined in general and on account of higher level topology the subject is put forward with specified descriptions, theorems, and detailed examples. The uniform spaces are examined as a whole with the parts named below respectively: Diagonal uniformities, uniform covers- an alternative approach to the uniform spaces; uniform products and subspaces. weak uniformities, uniformizability and uniform metrizability that focuses on which topologies come from uniformities and which uniformities come from metrics; complete uniform spaces and completeness in which the notion of completeness is carried over from the metrics spaces and given to the uniform spaces due to the generalized Cauchy sequence; the proximity spaces that introduce the "nearness relation". Finally the title of compactification and proximities aimed to establish the one-one correspondence between the compatible proximities on a Tychonoff space X and the compactification of XKeywords: Diagonal uniformities, uniform covers, weak uniformities, complete uniform spaces, proximity spaces.