The Foundations of Topological Analysis: A Straightforward Introduction
Book 2 Topological Ideas

This book is an introduction to the ideas from general topology that are used in elementary analysis.

K. G. Binmore (Author)

9780521299305, Cambridge University Press

Paperback, published 7 May 1981

264 pages
22.8 x 15.2 x 1 cm, 0.385 kg

This book is an introduction to the ideas from general topology that are used in elementary analysis. It is written at a level that is intended to make the bulk of the material accessible to students in the latter part of their first year of study at a university or college although students will normally meet most of the work in their second or later years. The aim has been to bridge the gap between introductory books like the author's Mathematical Analysis: A Straightforward Approach, in which carefully selected theorems are discussed at length with numerous examples, and the more advanced book on analysis, in which the author is more concerned with providing a comprehensive and elegant theory than in smoothing the ways for beginners. An attempt has been made throughout not only to prepare the ground for more advanced work, but also to revise and to illuminate the material which students will have met previously but may have not fully understood.

Introduction
13. Distance
14. Open and closed sets (I) 15. Open and closed sets (II)
16. Continuity
17. Connected sets
18. Cluster points
19. Compact sets (I)
20. Compact Sets (II)
21. Topology
22. Limits and continuity (I)
23. Limits and continuity (II)
24. Points at infinity
25. Sequences
26. Oscillation
27. Completeness
28. Series
29. Infinite sums
30. Separation in R n.

Subject Areas: Probability & statistics [PBT]