Abstract
We show that if $(X, \|. \|)$ is a separable Banach space, $\Omega \subset X$ is open, connected and $f: \Omega \to \mathbb{R}$ is an everywhere Gâteaux differentiable Lipschitz continuous function, then the graph of the derivative of $f$ is connected in $(\Omega,\| . \|)\times(X^\star , w^\star)$.
Citation
Tamás Mátrai. "Graphs of Gâteaux derivatives are w*-connected.." Real Anal. Exchange 29 (1) 291 - 298, 2003-2004.
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