Apartness Spaces as a Framework for Constructive Topology
Luminita Vîta (Dediu) and Douglas Bridges
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Abstract
An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.
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