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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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