Fibrewise Topology [Paperback]

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