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2005/2006 Differentiability as continuity.
David Gauld, Frédéric Mynard
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Real Anal. Exchange 31(2): 425-430 (2005/2006).

Abstract

We characterize differentiability of a map $f:\mathbb{R\rightarrow R}$ in terms of continuity of a canonically associated map $\widehat{f}$. To characterize pointwise differentiability of $f,$ both the domain and range of $\widehat{f}$ can be made topological. However, the global differentiability of $f$ is characterized by the continuity of $\widehat{f}$ whose domain is topological but whose range is a convergence space.

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David Gauld. Frédéric Mynard. "Differentiability as continuity.." Real Anal. Exchange 31 (2) 425 - 430, 2005/2006.

Information

Published: 2005/2006
First available in Project Euclid: 10 July 2007

zbMATH: 1146.26304
MathSciNet: MR2265784

Subjects:
Primary: 26A24, ‎54C30
Secondary: 26A06, 26A27, 54A10, 54A20

Rights: Copyright © 2005 Michigan State University Press

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