Brouwer Fixed Point Theorem in the General Case

  • Karol Pak
  • Published 2011 in Formalized Mathematics

Abstract

For simplicity, we adopt the following convention: n is a natural number, p, q, u, w are points of En T, S is a subset of En T, A, B are convex subsets of En T, and r is a real number. Next we state several propositions: (1) (1− r) · p+ r · q = p+ r · (q − p). (2) If u, w ∈ halfline(p, q) and |u− p| = |w − p|, then u = w. (3) Let given S. Suppose p ∈ S and… (More)
DOI: 10.2478/v10037-011-0024-3

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