Author | Lundell, Albert T. author |
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Title | The Topology of CW Complexes [electronic resource] / by Albert T. Lundell, Stephen Weingram |
Imprint | New York, NY : Springer New York, 1969 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-6254-8 |
Descript | VIII, 216 p. 10 illus. online resource |
0. Preliminaries -- I. Combinatorial Cell Complexes -- 1. Definitions -- 2. Examples -- 3. Carrier theory -- 4. Functions -- 5. Product complexes -- 6. Equivalence relations and quotients -- 7. Adjunction complexes -- II. CW Complexes -- 1. Definitions -- 2. Alternative descriptions of CW complexes -- 3. Remarks on the general topology of CW complexes -- 4. Paracompactness -- 5. Products, quotients, and adjunctions -- 6. Homotopy and local properties -- 7. The homotopy extension theorem -- 8. The cellular approximation theorem -- 9. Aspherical carrier theorem -- III. Regular and Semisimplicial CW Complexes -- 1. Regular and normal CW complexes -- 2. Regular CW complexes and invariance of domain -- 3. Semisimplicial complexes -- 4. The realization of semisimplicial complexes -- 5. Semisimplicial constructions -- 6. Simplicial subdivision of semisimplicial complexes -- 7. Barycentric subdivision of semisimplicial complexes -- 8. Regulated semisimplicial complexes -- 9. The functor * -- IV. Homotopy Type of CW Complexes -- 1. Homotopy equivalence and deformation retraction -- 2. Homotopy equivalence of adjunction spaces -- 3. Whiteheadโs theorems -- 4. Simplicial complexes with the metric topology -- 5. Equi-local convexity -- 6. Countable CW complexes -- 7. Finite CW complexes -- V. The Singular Homology of CW Complexes -- 1. Excision in the CW category -- 2. Cellular homology -- 3. Orientation, incidence, and degree -- 4. Regular CW complexes and proper maps -- 5. Quotient complexes -- 6. Product and adjunction complexes -- 7. Semisimplicial complexes -- 8. Realizing cellular maps -- Appendix I. Paracompact Spaces -- Appendix II. Extension Spaces and Neighborhood Retracts