Complements of Intersections in Constructive Mathematics

• Published in: Mathematical logic quarterly Vol. 40; no. 1; pp. 35 - 43
• Main Authors: Bridges, Douglas S., Ishihara, Hajime
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag Berlin GmbH 1994; WILEY‐VCH Verlag Berlin GmbH
• Subjects: Complements of intersections; Constructive mathematics; Intersect sharply; Markov's principle; Markovian counterexample; Metric complement

We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or fr...