Fixed Points : Mathematical World - Yu A. Shashkin

Fixed Points

By: Yu A. Shashkin

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Continuous mapping 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 mapping, 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 mapping; Continuous mappings of a sphere; Lemma in equality of degrees.

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