Properties of the Brouwer Degree

Robert F. Brown
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Robert F. Brown: University of California, Department of Mathematics

Chapter 9 in A Topological Introduction to Nonlinear Analysis, 2004, pp 55-61 from Springer

Abstract: Abstract This chapter is devoted to the properties of the Brouwer degree that we will need for the Leray-Schauder degree. In all that follows, we assume we have a map $$ f = \bar U \to R^n $$ such that F = f-1(0) is admissible in U, that is, compact and disjoint from ∂U, so the Brouwer degree d(f, U) is well-defined. The properties of the degree are given names for easy identification; the terminology I’m using for this purpose is pretty much standard. Some of the properties will carry over to the infinite-dimensional case and others are needed in order to make the transition to that more general setting. The following simple lemma will be helpful in verifying some of those properties.

Date: 2004
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DOI: 10.1007/978-0-8176-8124-1_9

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