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2007/2008 Functions for Which All Points Are Local Extrema
Ehrhard Behrends, Stefan Geschke, Tomasz Natkaniec
Real Anal. Exchange 33(2): 467-470 (2007/2008).

Abstract

Let $X$ be a connected separable linear order, a connected separable metric space, or a connected, locally connected complete metric space. We show that every continuous function $f:X\to\mathbb R$ with the property that every $x\in X$ is a local maximum or minimum of $f$ is in fact constant. We provide an example of a compact connected linear order $X$ and a continuous function $f:X\to\mathbb R$ that is not constant and yet every point of $X$ is a local minimum or maximum of $f$.

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Ehrhard Behrends. Stefan Geschke. Tomasz Natkaniec. "Functions for Which All Points Are Local Extrema." Real Anal. Exchange 33 (2) 467 - 470, 2007/2008.

Information

Published: 2007/2008
First available in Project Euclid: 18 December 2008

zbMATH: 1170.26002
MathSciNet: MR2458263

Subjects:
Primary: 26A15 , ‎54C30

Keywords: Continuous function , local extremum

Rights: Copyright © 2007 Michigan State University Press

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