Complements of Intersections in Constructive Mathematics

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...

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Bibliographic Details
Published inMathematical logic quarterly Vol. 40; no. 1; pp. 35 - 43
Main Authors Bridges, Douglas S., Ishihara, Hajime
Format Journal Article
LanguageEnglish
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
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Summary: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.
Bibliography:ark:/67375/WNG-4LVBGDDW-B
istex:69C87DA57AAB3A9C8B9150F64DF8439AF52A1314
ArticleID:MALQ19940400106
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.19940400106