Vol. 39, No. 3, 1971

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A geometric approach to the fixed point index

Roger David Nussbaum

Vol. 39 (1971), No. 3, 751–766

J. Leray defined a local fixed point index for functions defined in what he called convexoid spaces. From the standpoint of analysis, the most important example of a convexoid space is a compact subset C X,X a locally convex topological vector space, such that C = i=1nCi, where Ci are compact, convex subsets of X or a homeomorphic image of such a C. In this paper a simple geometric approach is given (see Lemma 2 below) by means of which a fixed point index can be defined for functions with domain in a class of spaces which contains the spaces C mentioned above and also the compact metric ANR’s. The usual properties of the fixed point index are established, and it is shown that they axiomatically determine the index for the class of spaces .

Mathematical Subject Classification 2000
Primary: 47H10
Secondary: 54H25
Received: 4 May 1970
Revised: 15 November 1970
Published: 1 December 1971
Roger David Nussbaum