Sequential, pointwise, and uniform continuity: A constructive note

Mathematical Logic Quarterly 39 (1):55-61 (1993)
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Abstract

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

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References found in this work

Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
Foundations of Constructive Mathematics.Michael J. Beeson - 1987 - Studia Logica 46 (4):398-399.
Computable Analysis.Oliver Aberth - 1984 - Journal of Symbolic Logic 49 (3):988-989.

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