Degree and index theories for noncompact function triples

Martin Väth


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.


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

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