### On Extendable Derivations

Tomasz Natkaniec
Source: Real Anal. Exchange Volume 34, Number 1 (2008), 207-214.

#### 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.

First Page:
Primary Subjects: 26A15
Secondary Subjects: 54C08
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Permanent link to this document: http://projecteuclid.org/euclid.rae/1242738931
Zentralblatt MATH identifier: 05578225
Mathematical Reviews number (MathSciNet): MR2527133

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