General Topology and Homotopy Theory

1. Front Matter

   Pages i-vii

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2. Introduction

   • I. M. James

   Pages 1-2

3. The Basic Framework

   • I. M. James

   Pages 3-30

4. The Axioms of Topology

   • I. M. James

   Pages 31-66

5. Spaces Under and Spaces Over

   • I. M. James

   Pages 67-107

6. Topological Transformation Groups

   • I. M. James

   Pages 108-136

7. The Notion of Homotopy

   • I. M. James

   Pages 137-166

8. Cofibrations and Fibrations

   • I. M. James

   Pages 167-197

9. Numerable Coverings

   • I. M. James

   Pages 198-223

10. Extensors and Neighbourhood Extensors

    • I. M. James

    Pages 224-243

11. Back Matter

    Pages 245-248

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Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group theory. This book is based on a course of 16 graduate lectures given at Oxford and elsewhere from time to time. In a course of that length one cannot discuss too many topics without being unduly superficial. However, this was never intended as a treatise on the subject but rather as a short introductory course which will, I hope, prove useful to specialists and non-specialists alike. The introduction contains a description of the contents. No algebraic or differen­ tial topology is involved, although I have borne in mind the needs of students of those branches of the subject. Exercises for the reader are scattered throughout the text, while suggestions for further reading are contained in the lists of references at the end of each chapter. In most cases these lists include the main sources I have drawn on, but this is not the type of book where it is practicable to give a reference for everything.

• Homotopy
• cofibration
• fibrations
• group theory
• homotopy theory

• Mathematical Institute, Oxford University, Oxford, England

  I. M. James