This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
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Book Description
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type.
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First Sentence:
Balls and balloons are the standard models for the cells used in the theory of CW-complexes; thus, the chapter starts by 'playing' a bit with such toys. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
anodyne extension, closed cofibration, final topology with respect, cosimplicial set, fibre homotopic, simplicial homotopy equivalences, simplicial subset, minimal fibration, segment with vertices, acyclic fibration, many closed cells, singular functor, realizability theorem, homotopy equivalence iff, simplicial map, cell subcomplex, underlying polyhedron, adjunction spaces, barycentric refinement, normal subdivision, homotopy rel, weak homotopy equivalence, strong deformation retract, ordered simplicial complex, degeneracy operators Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Take, Proof Define, Dieter Puppe, Proof Choose, Proof See Proposition New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Balls and balloons are the standard models for the cells used in the theory of CW-complexes; thus, the chapter starts by 'playing' a bit with such toys. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
anodyne extension, closed cofibration, final topology with respect, cosimplicial set, fibre homotopic, simplicial homotopy equivalences, simplicial subset, minimal fibration, segment with vertices, acyclic fibration, many closed cells, singular functor, realizability theorem, homotopy equivalence iff, simplicial map, cell subcomplex, underlying polyhedron, adjunction spaces, barycentric refinement, normal subdivision, homotopy rel, weak homotopy equivalence, strong deformation retract, ordered simplicial complex, degeneracy operators Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Take, Proof Define, Dieter Puppe, Proof Choose, Proof See Proposition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 19
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7
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- Elements of Modern Topology by R. Brown in Back Matter
- Dimension Theory (Princeton Mathematical Ser.; Vol 4) by Witold Hurewicz in Back Matter
- Choquet Order and Simplices With Applications in Probabilistic Models (Lecture Notes in Mathematics) by Gerhard Winkler in Back Matter
- Algebraic Topology: An Introduction (Graduate Texts in Mathematics) (v. 56) by William S. Massey in Back Matter
- A Course in Homological Algebra (Graduate Texts in Mathematics) by Peter J. Hilton in Back Matter
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- Infinite Homotopy Theory (K-Monographs in Mathematics, Volume 6) by H-J. Baues in Back Matter
- Frontiers of Human-Centred Computing, Online Communities and Virtual Environments by Rae Earnshaw on page 339
- Topologie: 2. Vollig Neu Bearbeitete Und Erweiterte Auflage (De Gruyter Lehrbuch) (German Edition) by Tammo Tom Dieck in Back Matter
- Acta Numerica 2002: Volume 11 by Arieh Iserles on page 332
- Abstract Homotopy and Simple Homotopy Theory by Klaus Heiner Kamps in Back Matter
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