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Beskrivning
This volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
ONE METRIC SPACES1 Open and closed sets 2 Completeness 3 The real line 4 Products of metric spaces 5 Compactness 6 Continuous functions 7 Normed linear spaces 8 The contraction principle 9 The Frechet derivative TWO TOPOLOGICAL SPACES 1 Topological spaces 2 Subspaces 3 Continuous functions 4 Base for a topology 5 Separation axioms 6 Compactness 7 Locally compact spaces 8 Connectedness 9 Path connectedness 10 Finite product spaces 11 Set theory and Zorn's lemma 12 Infinite product spaces 13 Quotient spaces THREE HOMOTOPY THEORY 1 Groups 2 Homotopic paths 3 The fundamental group 4 Induced homomorphisms 5 Covering spaces 6 Some applications of the index7 Homotopic maps 8 Maps into the punctured plane 9 Vector fields 10 The Jordan Curve Theorem FOUR HIGHER DIMENSIONAL HOMOTOPY1 Higher homotopy groups 2 Noncontractibility of Sn3 Simplexes and barycentric subdivision4 Approximation by piecewise linear maps5 Degrees of mapsBIBLIOGRAPHYLIST OF NOTATIONSSOLUTIONS TO SELECTED EXERCISESINDEX
