Vol. 35, No. 3, 1970

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An elementary proof of the uniqueness of the fixed point index

Robert F. Brown

Vol. 35 (1970), No. 3, 549–558
Abstract

In 1953, Barrett O’Neill stated axioms for a “fixed point index” and obtained existence and uniqueness theorems for the index on finite polyhedra. The proof of uniqueness consisted of showing that any function which satisfied the axioms must agree with the index he had already defined. This paper presents a proof of the uniqueness of the fixed point index on finite polyhedra which depends only on the axioms and therefore is “elementary” in the sense that it is independent of the existence of an index. The proof is “elementary” also in that all the techniques used are taken from geometric topology or calculus so that, in particular, no algebraic topology is required. An elementary proof of the uniqueness of the fixed point index on compact metric absolute neighborhood retracts is an immediate consequence of the material in this paper.

Mathematical Subject Classification
Primary: 55.36
Milestones
Received: 21 February 1969
Published: 1 December 1970
Authors
Robert F. Brown
Department of Mathematics
University of California, Los Angeles
Los Angeles CA 90095-1555
United States
http://www.math.ucla.edu/~rfb/