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2005/2006 Vertically rigid functions.
Brandi Cain, John Clark, David Rose
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Real Anal. Exchange 31(2): 515-518 (2005/2006).

Abstract

A function $f\colon{\mathbb{R}}\to{\mathbb{R}}$ is said to be vertically rigid provided its graph $G(f)=\{{\langle} x,f(x){\rangle}\colon x\in{ \mathbb{R}}\}$ is isometric with the graph of the function $kf$ for every non-zero $k\in{\mathbb{R}}$. We show that the group homomorphisms $f$ from ${ \langle}{\mathbb{R}},+{\rangle}$ into ${\langle}{\mathbb{R}}^+,\cdot{\rangle} $ is vertically rigid if and only if it is an epimorphism. Some other examples of vertically rigid functions will also be given. A problem of characterizing all vertically rigid functions remains open.

Citation

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Brandi Cain. John Clark. David Rose. "Vertically rigid functions.." Real Anal. Exchange 31 (2) 515 - 518, 2005/2006.

Information

Published: 2005/2006
First available in Project Euclid: 10 July 2007

zbMATH: 1103.54010
MathSciNet: MR2265791

Subjects:
Primary: ‎54C30
Secondary: 33B10, 51M04, 54A10

Rights: Copyright © 2005 Michigan State University Press

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