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Apartness and Uniformity
Synopsis We first introduce the notion of a (pre-)apartness between points and subsets in an abstract space X, and derive some elementary properties from our axioms. Each point-set pre-apartness gives rise to a topology-the apartness topology-on X, and to several constructively distinct continuity properties, which are explored in Section 2.3. Limits and the Hausdorff property are discussed in Section 2.4, and product pre-apartness spaces in Section 2.5. In the final section we discuss the roledoi:10.1007/978-3-642-22415-7_2 fatcat:2ypa5axwgrcb3j7slejdwodr7u