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Ein Vortrag im Rahmen des Siegener Tagess der konstruktive Analysis.

In this talk I first clarify what is meant by constructive mathematics (à la Bishop). Then I introduce the notion of apartness: first between points and sets, and secondly between sets and sets. The axiomatic theory of apartness spaces, begun by me and Luminita Simona Vîta in 2000 and subsequently taken up by a number of other mathematicians, provides a robust constructive framework for topology and the theory of uniform spaces. I will present the fundamentals of the theory, leading to the more interesting set-set case and revealing the interplay between apartness and uniform structures.

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