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High Quality Content by WIKIPEDIA articles! In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are "isolated" from each other in a certain sense. Given a set X: the discrete topology on X is defined by letting every subset of X be open, and X is a discrete topological space if it is equipped with its discrete topology; the discrete uniformity on X is defined by letting every superset of the diagonal {(x,x) : x is in X} in X × X be an entourage, and X is a discrete uniform space if it is equipped with its discrete uniformity.