2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73734Theorem: 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 dim{x in X : Phi(x)=Psi(x)} >= dim(Phi^{-1}(0)). Here dim denotes the covering dimension.3 pagesFunctional Analysis47J05, 47H10text