### 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.

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.

#### Keywords

Fixed point index; degree theory; multivalued map; fundamental set; countably condensing map; nonconvex domain; ANR; measure of noncompactness; Skrypnik degree

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