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Introduction to the Analysis of Metric Spaces

by John R. Giles

Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated.

FORMAT
Paperback
LANGUAGE
English
CONDITION
Brand New


Publisher Description

Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated.

Table of Contents

Preface; Part I. Metric Spaces and Normed Linear Spaces: 1. Definitions and examples; 2. Balls and boundedness; Part II. Limit Processes: 3. Convergence and completeness; 4. Cluster points and closure; 5. Application: Banach's fixed point theorem; Part III. Continuity: 6. Continuity in metric spaces; 7. Continuous linear mappings; Part IV. Compactness: 8. Sequential compactness in metric spaces; 9. Continuous functions on compact metric spaces; Part V. The Metric Topology: 10. The topological analysis of metric spaces; Appendices; Index of notation; Index.

Description for Bookstore

An introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. The student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. Graded exercises are provided.

Description for Library

An introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. The student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. Graded exercises are provided.

Details

ISBN0521359287
Author John R. Giles
Short Title INTRO TO THE ANALYSIS OF METRI
Pages 272
Publisher Cambridge University Press
Series Australian Mathematical Society Lecture Series
Language English
ISBN-10 0521359287
ISBN-13 9780521359283
Media Book
Format Paperback
DEWEY 514.3
Series Number 03
Illustrations Yes
Year 1987
Publication Date 1987-12-31
Imprint Cambridge University Press
Place of Publication Cambridge
Country of Publication United Kingdom
DOI 10.1604/9780521359283
Audience College/Higher Education
UK Release Date 1987-09-03
AU Release Date 1987-09-03
NZ Release Date 1987-09-03

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