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Sequential Continuity of Functions in Constructive Analysis
Author(s) -
Bridges Douglas,
Mahalanobis Ayan
Publication year - 2000
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/(sici)1521-3870(200001)46:1<139::aid-malq139>3.0.co;2-b
Subject(s) - mathematics , omniscience , bounded function , constructive , interval (graph theory) , bounded variation , markov chain , discrete mathematics , function (biology) , calculus (dental) , pure mathematics , combinatorics , mathematical analysis , process (computing) , computer science , statistics , philosophy , medicine , dentistry , evolutionary biology , biology , operating system , theology
It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.