Fibrewise Topology

The aim of this book is to promote a fibrewise perspective, particularly in topology.

I. M. James (Author)

9780521089258, Cambridge University Press

Paperback / softback, published 30 October 2008

212 pages
22.9 x 15.2 x 1.2 cm, 0.32 kg

The aim of this book is to promote a fibrewise perspective, particularly in topology, which is central to modern mathematics. Already this view is standard in the theory of fibre bundles and therefore in such subjects as global analysis. It has a role to play also in general and equivariant topology. There are strong links with equivariant topology, a topic which has latterly been subject to great research activity. It is to be hoped that this book will provide a solid and invigorating foundation for the increasing research interest in fibrewise topology

Preface
Part I. Basic Fibrewise Topology: 1. Fibrewise topological spaces
2. Fibrewise separation conditions
3. Fibrewise compact spaces
4. Tied filters
5. Fibrewise quotient spaces
6. Fibrewise pointed topological spaces
7. Relation with equivariant topology
Part II. Further Fibrewise Topology: 8. Fibrewise compactification
9. The fibrewise mapping-space
10. Fibrewise compactly-generated spaces
11. Naturality and naturalization
Part III. Fibrewise Uniform Spaces: 12. Fibrewise uniform structures
13. Fibrewise uniform topology
14. The Cauchy completion
15. Fibrewise completion
16. Functoriality
17. Fibrewise compactness and precompactness
Part IV. Fibrewise Homotopy Theory: 18. Fibrewise homotopy
19. Fibrewise pointed homotopy
20. Fibrewise confibrations
21. Fibrewise pointed confibrations
22. Fibrewise non-degenerate spaces
23. Fibrewise fibrations
24. Relation with equivariant homotopy theory
Part V. Miscellaneous Topics: 25. Fibre bundles
26. Numerable coverings
27. Fibrewise connectedness
Note on the literature
References
Index.

Subject Areas: Algebraic topology [PBPD]