Real Analysis Exchange

The Darboux property for gradients

Jan Malý

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It is well known that the derivative of a function of one variable has the Darboux property. In this paper it is shown that the gradient of a differentiable function of several variables maps certain closed convex sets to connected sets.

Article information

Real Anal. Exchange, Volume 22, Number 1 (1996), 167-173.

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26B05: Continuity and differentiation questions

Darboux property differentiable gradient


Malý, Jan. The Darboux property for gradients. Real Anal. Exchange 22 (1996), no. 1, 167--173.

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