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A Generalization of the Mapping Degree

Published online by Cambridge University Press:  20 November 2018

D. G. Bourgin
D. G. Bourgin*
Affiliation:
University of Houston, Houston, Texas
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For the single-valued case the notion of degree has been given recent expression by papers of Dold [5] for the finite dimensional case, and by Leray-Schauder [8] for the locally convex linear topological space. Klee [7] has removed this restriction by use of shrinkable in place of convex neighborhoods with the central role filled by a form of (2.15) below. For set-valued maps a modern formulation is, for instance, to be found in Gorniewicz-Granas [6]. These contributions relate the degree to the Lefschetz number, and the set-valued maps are required to map points into acyclic sets; that is to say, into "swollen points".

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1109 - 1117
Copyright
Copyright © Canadian Mathematical Society 1974

References

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