T.W. Gamelin

Introduction to Topology

Second Edition

• Broschiertes Buch

Produktbeschreibung

This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

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Produktdetails

• Dover Books on Mathema 1.4tics
• Verlag: Dover Publications Inc.
• 2nd edition
• Seitenzahl: 256
• Erscheinungstermin: 16. Februar 1999
• Englisch
• Abmessung: 237mm x 154mm x 14mm
• Gewicht: 376g
• ISBN-13: 9780486406800
• ISBN-10: 0486406806
• Artikelnr.: 22203466

Inhaltsangabe

ONE METRIC SPACES 1 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 index 7
Homotopic maps 8 Maps into the punctured plane 9 Vector fields 10 The
Jordan Curve Theorem FOUR HIGHER DIMENSIONAL HOMOTOPY 1 Higher homotopy
groups 2 Noncontractibility of Sn 3 Simplexes and barycentric subdivision 4
Approximation by piecewise linear maps 5 Degrees of maps BIBLIOGRAPHY LIST
OF NOTATIONS SOLUTIONS TO SELECTED EXERCISES INDEX