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1996/1997 Darboux like functions
Richard G. Gibson, Tomasz Natkaniec
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Real Anal. Exchange 22(2): 492-533 (1996/1997).


A function \(f:\mathbb{R}\to\mathbb{R}\) is said to have the intermediate value property provided that if \(p\) and \(q\) are real numbers such that \(p\neq q\) and \(f(p)\lt f(q)\), then for every \(y\in (f(p),f(q))\) there exists a number \(x\) between \(p\) and \(q\) with \(f(x)=y\). In 1875, G. Darboux showed that there exist functions with the intermediate value property that are not continuous \cite{22}. Because of his work with functions having the intermediate value property, these functions are called Darboux functions.


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Richard G. Gibson. Tomasz Natkaniec. "Darboux like functions." Real Anal. Exchange 22 (2) 492 - 533, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0942.26004
MathSciNet: MR1460971

Primary: 26A15
Secondary: ‎54C30

Keywords: almost continuous functions , CIVP-functions , connectivity functions , Darboux functions , DIVP-functions , extendable functions , functions with perfect road , peripherally continuous functions , property (\(B\)) , SCIVP-functions , Sierpiński-Zygmund functions , WCIVP-functions

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
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