UID:
almahu_9948197631102882
Umfang:
1 online resource (xxxvii, 339 pages) :
,
illustrations.
ISBN:
9780470067949
,
0470067942
,
9780470067932
,
0470067934
,
9781118626221
,
1118626222
Serie:
Pure and applied mathematics
Anmerkung:
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.
Weitere Ausg.:
Print version: Basener, William F., 1973- Topology and its applications. Hoboken, N.J. : Wiley-Interscience, ©2006 ISBN 9780471687559
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Electronic books.
;
Electronic books.
;
Textbooks.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9780470067949
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