✦ LIBER ✦

Complements of Intersections in Constructive Mathematics

✍ Scribed by Douglas S. Bridges; Hajime Ishihara

Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 488 KB
Volume: 40
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19940400106

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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 from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and the completeness of metric spaces.

Mathematics Subject Classification: 03F65, 46S30.

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