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A Definitive Constructive Open Mapping Theorem?
Author(s) -
Bridges Douglas,
Ishihara Hajime
Publication year - 1998
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.19980440413
Subject(s) - constructive , mathematics , constructive proof , hilbert space , context (archaeology) , algebra over a field , calculus (dental) , pure mathematics , discrete mathematics , computer science , process (computing) , medicine , paleontology , dentistry , biology , operating system
It is proved, within Bishop's constructive mathematics (BISH), that, in the context of a Hilbert space, the Open Mapping Theorem is equivalent to a principle that holds in intuitionistic mathematics and recursive constructive mathematics but is unlikely to be provable within BISH.