Degree and index theories for noncompact function triples

Abstract

We describe a very general procedure how one may extend an arbitrary degree or index theory (originally defined only for compact maps) also for large classes of noncompact maps. We also show how one may obtain degree or index theories relative to some set. Our results even apply to the general setting when one has a combined degree and index theory for function triples. The results are applied to countably condensing perturbations of monotone maps.