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