and Luminit¸a Vît¸ă, ‘Apartness spaces as a foundation for constructive topology (0)

by Douglas Bridges
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A Constructive Theory of Point-Set Nearness

by Luminita Vita, Douglas Bridges - in Proceedings of Topology in Computer Science: Constructivity; Asymmetry and Partiality; Digitization, Seminar in Dagstuhl, Germany, 4–9 June 2000; Springer Lecture Notes in Computer Science , 2001
"... An axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for topology. ..."
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An axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for topology.

Separatedness in Constructive Topology

by Douglas Bridges, et al. - DOCUMENTA MATH. , 2003
"... We discuss three natural, classically equivalent, Hausdorff separation properties for topological spaces in constructive mathematics. Using Brouwerian examples, we show that our results are the best possible in our constructive framework. ..."
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We discuss three natural, classically equivalent, Hausdorff separation properties for topological spaces in constructive mathematics. Using Brouwerian examples, we show that our results are the best possible in our constructive framework.