Abstract. The purpose of this paper is to define a uniformity on a frame using entourages. A definition of uniformities in terms of covers has been given by A. PULTR ([8], [10]). We introduce two new symmetry conditions for a quasi-uniform space, open-set symmetry and small-set symmetry. We prove that a quasi-uniformity ~ is a uniformity if and only if it is both open-set symmetric and small-set symmetric. The category of (covering) uniform frames is isomorphic with the category of entourage uniform frames.

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The purpose of this paper is to develop a general technique for