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The theory of fixed points belongs to topology, a part of mathematics created at the end of the nineteenth century, and makes extensive use of such topological notions as continuity, compactness, homotopy and the degree of a mapping. The subject of this book is essentially one single problem: whether a closed interval, square, disc or sphere has the fixed point property. *Contents Continuous mappings of a closed interval and a square; First combinato-rial 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 interme- diate 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; Theorem on equality of degrees; Solutions and answers; References. 88pp. (1998) 230 × 150mm ISBN 978 81 7371 1206
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Pages : 88
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