On the homotopy property of degree for multivalued noncompact maps

Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].

On the homotopy property of degree for multivalued noncompact maps

Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].