### A Borsuk-type theorem for some classes of perturbed Fredholm maps

#### Abstract

We prove an odd mapping theorem of Borsuk type for locally

compact perturbations of Fredholm maps of index zero between Banach spaces.

We extend this result to a more general class of perturbations of Fredholm

maps, defined in terms of measure of noncompactness.

compact perturbations of Fredholm maps of index zero between Banach spaces.

We extend this result to a more general class of perturbations of Fredholm

maps, defined in terms of measure of noncompactness.

#### Keywords

Oriented Fredholm maps; Borsuk odd mapping theorem; topological degree; measure of noncompactness; $\alpha$-contractive maps

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