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


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.


Download Citation

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


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

zbMATH: 1146.26304
MathSciNet: MR2265784

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

Keywords: continuity , convergence spaces , differentiability , real valued functions

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 2 • 2005/2006
Back to Top