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