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On the topological dimension of the solution set of a class of nonlinear equations. (English. Abridged French version) Zbl 0884.47043
Let $$X$$ and $$Y$$ be two Banach spaces, $$\Phi: X\to Y$$ a continuous linear surjective map, and $$\Psi: X\to Y$$ a continuous compact map. The author proves that the topological dimension of the set $$\{x:x\in X,\;\Phi(x)=\Psi(x)\}$$ is not less than that of the nullspace of $$\Phi$$.

##### MSC:
 47J05 Equations involving nonlinear operators (general) 47H99 Nonlinear operators and their properties 54F45 Dimension theory in general topology
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