Description

Book Synopsis
Presents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.

Table of Contents
Continuous mappings of a closed interval and a square First combinatorial lemma Second combinatorial lemma, or walks through the rooms in a house Sperner's lemma Continuous mappings, homeomorphisms, and the fixed point property Compactness Proof of Brouwer's Theorem for a closed interval, the intermediate value theorem, and applications Proof of Brouwer's Theorem for a square The iteration method Retraction Continuous mappings of a circle, homotopy, and degree of a mapping Second definition of the degree of a mapping Continuous mappings of a sphere Lemma on equality of degrees.

Fixed Points

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    A Paperback by American Mathem American Mathem

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 12/30/1991 12:00:00 AM
      ISBN13: 9780821890004, 978-0821890004
      ISBN10: 082189000X
      Also in:
      Mathematics Topology

      Description

      Book Synopsis
      Presents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.

      Table of Contents
      Continuous mappings of a closed interval and a square First combinatorial lemma Second combinatorial lemma, or walks through the rooms in a house Sperner's lemma Continuous mappings, homeomorphisms, and the fixed point property Compactness Proof of Brouwer's Theorem for a closed interval, the intermediate value theorem, and applications Proof of Brouwer's Theorem for a square The iteration method Retraction Continuous mappings of a circle, homotopy, and degree of a mapping Second definition of the degree of a mapping Continuous mappings of a sphere Lemma on equality of degrees.

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