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Leray-Schauder Degree and Fixed Point Index

  • Andrzej Granas
  • James Dugundji
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This chapter is devoted to the concept of the topological degree and the fixed point index. With the aid of some fairly elementary facts from linear algebra and simplicial topology, we develop first the theory in the simple setting of Euclidean space. Then, using some of the techniques developed in Chapter II, we extend the index in R n to infinite dimensions, and establish the fixed point index theory for compact maps in arbitrary metric ANRs. As a special case we also obtain the Leray-Schauder degree for compact fields in normed linear spaces. The chapter ends with a number of applications.

Keywords

Normed Linear Space Point Index Topological Degree Polyhedral Domain Absolute Retract 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Andrzej Granas
    • 1
    • 2
  • James Dugundji
  1. 1.Département de Mathématiques et StatistiqueUniversité de MontréalMontréalCanada
  2. 2.Department of Mathematics and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland

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