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.
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Keywords: additive function ; derivation ; almost continuity ; extendability ; algebraically independent sets
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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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