## Real Analysis Exchange

### Darboux like functions

#### 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.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 2 (1996), 492-533.

Dates
First available in Project Euclid: 22 May 2012

https://projecteuclid.org/euclid.rae/1337713140

Mathematical Reviews number (MathSciNet)
MR1460971

Zentralblatt MATH identifier
0942.26004

#### Citation

Gibson, Richard G.; Natkaniec, Tomasz. Darboux like functions. Real Anal. Exchange 22 (1996), no. 2, 492--533. https://projecteuclid.org/euclid.rae/1337713140

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