Complements of Intersections in Constructive Mathematics
Douglas Bridges, Hajime Ishihara · Mathematical logic quarterly · 1994
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.