Real Analysis Exchange

An example of a Darboux function having no fixed points.

Zbigniew Grande

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In this article we construct an example of a bilaterally quasicontinuous Darboux function \(f:[0,1] \to [0,1]\), which has no fixed points.

Article information

Real Anal. Exchange, Volume 28, Number 2 (2002), 375-380.

First available in Project Euclid: 20 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A05 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

Density topology condition \((s_1)\) quasicontinuity fixed point of mapping.


Grande, Zbigniew. An example of a Darboux function having no fixed points. Real Anal. Exchange 28 (2002), no. 2, 375--380.

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