Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- PART I ELEMENTS OF REAL ANALYSIS
- PART II ELEMENTS OF ABSTRACT ANALYSIS
- 10 Point set topology
- 11 Metric spaces
- 12 Complete metric spaces
- 13 Some applications of completeness
- 14 Linear operators
- 15 Differential calculus on ℝn
- 16 Function space topologies
- Appendix A Vector spaces
- Appendix B The b-adic representation of numbers
- Appendix C Finite, denumerable, and uncountable sets
- Appendix D The syntax of mathematical languages
- References
- Index
12 - Complete metric spaces
from PART II - ELEMENTS OF ABSTRACT ANALYSIS
Published online by Cambridge University Press: 05 January 2013
Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- PART I ELEMENTS OF REAL ANALYSIS
- PART II ELEMENTS OF ABSTRACT ANALYSIS
- 10 Point set topology
- 11 Metric spaces
- 12 Complete metric spaces
- 13 Some applications of completeness
- 14 Linear operators
- 15 Differential calculus on ℝn
- 16 Function space topologies
- Appendix A Vector spaces
- Appendix B The b-adic representation of numbers
- Appendix C Finite, denumerable, and uncountable sets
- Appendix D The syntax of mathematical languages
- References
- Index
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- Real Analysis through Modern Infinitesimals , pp. 404 - 432Publisher: Cambridge University PressPrint publication year: 2011