Covering dimension and nonlinear equations
Abstract
Theorem: Let X and Y be two Banach spaces, Phi: X to Y a continuous, linear, surjective operator, and Psi: X to Y a completely continuous operator with bounded range. Then, one has dimx in X : Phi(x)=Psi(x) >= dim(Phi-1(0)). Here dim denotes the covering dimension.
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