Real Analysis Exchange

On Extendable Derivations

Tomasz Natkaniec

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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.

Article information

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

Dates
First available: 19 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.rae/1242738931

Zentralblatt MATH identifier
05578225

Mathematical Reviews number (MathSciNet)
MR2527133

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 54C08: Weak and generalized continuity

Keywords
additive function derivation almost continuity extendability algebraically independent sets

Citation

Natkaniec, Tomasz. On Extendable Derivations. Real Analysis Exchange 34 (2008), no. 1, 207--214. http://projecteuclid.org/euclid.rae/1242738931.


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