The Darboux property for gradients

Jan Malý

doi:rae/1338515211

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Home > Journals > Real Anal. Exchange > Volume 22 > Issue 1 > Article

1996/1997 The Darboux property for gradients

Jan Malý

Author Affiliations +

Jan Malý¹
¹Department of Mathematical Analysis

Real Anal. Exchange 22(1): 167-173 (1996/1997).

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Abstract

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.