First Course in Metric Spaces

B. K. Tyagi

doi:10.1017/UPO9788175968608

First Course in Metric Spaces presents a systematic and rigorous treatment of the subject of Metric Spaces which are mathematical objects equipped with the notion of distance. This book is a step towards the preparation for the study of more advanced topics in Analysis such as Topology. The contents are primarily suitable for teaching at the graduate level and serve as a treatise for undergraduate and postgraduate students. The book discusses classification of Metric Spaces using the standard classification notions such as completeness, compactness, and connectedness. The book also contains chapters on limit and continuity of mappings, fixed points and approximations, and a complete ordered field of real numbers obtained from cauchy sequences of rational numbers. Each chapter is interspersed with many examples and exercises.

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First Course in Metric Spaces

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Contents

Frontmatter
pp i-iv

Preface
pp v-viii

Contents
pp ix-xii

1 - Preliminaries
pp 1-85

2 - Basic Concepts in Metric Spaces
pp 86-152

3 - Sequences in Metric Spaces
pp 153-162

4 - Limits and Continuity
pp 163-207

5 - Completeness
pp 208-245

6 - Compactness
pp 246-278

7 - Connectedness
pp 279-304

8 - Approximations
pp 305-318

9 - Fixed Point Theorems and Their Applications
pp 319-332

10 - A Construction of Real Number System
pp 333-346

Appendix A - Definition of Sets as Cumulative Type Structures
pp 347-347

Appendix B - Bibliography
pp 348-349

Index
pp 350-352

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