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Sequential, pointwise, and uniform continuity: A constructive note
Author(s) -
Bridges Douglas S.
Publication year - 1993
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.19930390108
Subject(s) - pointwise , mathematics , constructive , uniform limit theorem , remainder , uniform continuity , regular polygon , continuous function (set theory) , constructive proof , pointwise convergence , pure mathematics , function (biology) , discrete mathematics , calculus (dental) , metric space , mathematical analysis , process (computing) , arithmetic , computer science , dentistry , evolutionary biology , biology , operating system , medicine , approx , geometry
The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real‐valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.