Brouwer in Higher Dimensions

The Brouwer Fixed-Point Theorem in All Finite Dimensions
  • Joel H. Shapiro
Part of the Universitext book series (UTX)


Having discussed the Brouwer Fixed-Point Theorem (Chap.  1) and proved it for triangles (Chap.  2), we’re ready to prove it in every dimension for closed balls and even for compact, convex sets. Our proof will be quite different from that of Chap.  2, with the combinatorics of Sperner’s Lemma replaced by methods of analysis.


Unit Circle Closed Unit Ball Closed Unit Disc Infinite Dimensional Hilbert Space Reverse Triangle Inequality 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Joel H. Shapiro
    • 1
  1. 1.Portland State UniversityPortlandUSA

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