Kooperativer Bibliotheksverbund

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Format: 1 online resource (xxxvii, 339 pages) : , illustrations.

ISBN: 9780470067949 , 0470067942 , 9780470067932 , 0470067934 , 9781118626221 , 1118626222

Series Statement: Pure and applied mathematics

Note: Front Matter -- Continuity -- Compactness and Connectedness -- Manifolds and Complexes -- Homotopy and the Winding Number -- Fundamental Group -- Homology -- Appendix A: Knot Theory -- Appendix B: Groups -- Appendix C: Perspectives in Topology -- References -- Index -- Pure and Applied Mathematics. , Preface -- , Introduction -- , Preliminaries -- , Cardinality -- , Continuity -- , Continuity and open sets in R n -- , Continuity and open sets in topological spaces -- , Metric, product, and quotient topologies -- , Subsets of topological spaces -- , Continuous functions and topological equivalence -- , Surfaces -- , Application : chaos in dynamical systems -- , History of chaos -- , A simple example -- , Notions of chaos -- , Compactness -- , Closed bounded subsets of R -- , Compact spaces -- , Identification spaces and compactness -- , Connectedness and path-connectedness -- , Cantor sets -- , Application : compact sets in population dynamics and fractals -- , Manifolds and complexes -- , Manifolds -- , Triangulations -- , Classification of surfaces -- , Gluing disks -- , Planar models -- , Classification of surfaces -- , Euler characteristic -- , Topological groups -- , Group actions and orbit spaces -- , Flows on tori -- , Robotic coordination and configuration spaces -- , Geometry of manifolds -- , The topology of the universe. , Homotopy and the winding number -- , Homotopy and paths -- , The winding number -- , Degrees of maps -- , The Brouwer fixed point theorem -- , The Borsuk-Ulam theorem -- , Vector fields and the Poincaré index theorem -- , Applications 1 -- , The fundamental theorem of algebra -- , Sandwiches -- , Game theory and Nash equilibria -- , Applications 2 : calculus -- , Vector fields, path integrals, and the winding number -- , Vector fields on surfaces -- , Index theory for n-symmetry fields -- , Index theory in computer graphics -- , Fundamental group -- , Definition and basic properties -- , Homotopy equivalence and retracts -- , The fundamental group of spheres and tori -- , The Seifert-van Kampen theorem -- , Flowers and surfaces -- , The Seifert-van Kampen theorem -- , Covering spaces -- , Group actions and deck transformations -- , Applications -- , Order and emergent patterns in condensed matter physics. , Homology -- , [triangle]-complexes -- , Chains and boundaries -- , Examples and computations -- , Singular homology -- , Homotopy invariance -- , Brouwer fixed point theorem for D n -- , Homology and the fundamental group -- , Betti numbers and the Euler characteristic -- , Computational homology-- , Computing Betti numbers -- , Building a filtration -- , Persistent homology -- , Appendix A : Knot theory -- , Appendix B : Groups -- , Appendix C : Perspectives in topology -- , Point set topology -- , Geometric topology -- , Algebraic topology -- , Combinatorial topology -- , Differential topology -- , References -- , Bibliography-- , Index.

Additional Edition: Print version: Basener, William F., 1973- Topology and its applications. Hoboken, N.J. : Wiley-Interscience, ©2006 ISBN 9780471687559

Language: English

Subjects: Mathematics

Keywords: Electronic books. ; Electronic books. ; Textbooks.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9780470067949