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Constructive complements of unions of two closed sets
Author(s) -
Bridges Douglas S.
Publication year - 2004
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.200410093
Subject(s) - mathematics , constructive , complement (music) , closure (psychology) , completeness (order theory) , dual (grammatical number) , space (punctuation) , order (exchange) , mathematical economics , pure mathematics , algebra over a field , discrete mathematics , calculus (dental) , law , computer science , political science , business , mathematical analysis , linguistics , process (computing) , philosophy , dentistry , chemistry , operating system , biochemistry , medicine , finance , complementation , gene , phenotype
It is well known that in Bishop‐style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)