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Complements of Intersections in Constructive Mathematics
Author(s) -
Bridges Douglas S.,
Ishihara Hajime
Publication year - 1994
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19940400106
Subject(s) - mathematics , constructive , metric space , completeness (order theory) , mathematics subject classification , perspective (graphical) , space (punctuation) , metric (unit) , pure mathematics , relation (database) , element (criminal law) , discrete mathematics , algebra over a field , calculus (dental) , mathematical analysis , computer science , law , geometry , operations management , process (computing) , database , political science , economics , operating system , medicine , dentistry
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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