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

by K. G. Binmore

• ISBN13: 9780521299305
• ISBN10: 0521299306
• Format: Paperback
• Copyright: 1981-06-30
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction

Distance

Open and closed sets (I)

Open and closed sets (II)

Continuity

Connected sets

Cluster points

Compact sets (I)

Compact Sets (II)

Topology

Limits and continuity (I)

Limits and continuity (II)

Points at infinity

Sequences

Oscillation

Completeness

Series

Infinite sums

Separation in R n

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