Abstract
There are derivations $f : \mathbb{R} \to \mathbb{R}$ which are almost continuous in the sense of Stallings but not extendable. Every derivation $f : \mathbb{R} \to \mathbb{R}$ can be expressed as the sum of two extendable derivations, as the discrete limit of a sequence of extendable derivations and as the limit of a transfinite sequence of extendable derivations. Analogous results hold for additive functions.
Citation
Tomasz Natkaniec. "On Extendable Derivations." Real Anal. Exchange 34 (1) 207 - 214, 2008/2009.
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