Metric Space Topology: Examples, Exercises and Solutions

✍ Scribed by Wing-Sum Cheung

• Year: 2023
• Tongue: English
• Leaves: 442
• Series: Series on Analysis, Applications and Computation 12
• Category: Library

✦ Table of Contents

Contents
Preface
A Note on the Convention
About the Author
1. Metric Spaces
1.1 Definitions and Examples
Exercise 1.1
Part A: True or False Questions
Part B: Problems
1.2 Topology of Metric Spaces
Exercise 1.2
Part A: True or False Questions
Part B: Problems
1.3 Compactness
Exercise 1.3
Part A: True or False Questions
Part B: Problems
1.4 Compactness in the Euclidean Space Rn
Exercise 1.4
Part A: True or False Questions
Part B: Problems
2. Limits and Continuity
2.1 Convergence in a Metric Space
Exercise 2.1
Part A: True or False Questions
Part B: Problems
2.2 Complete Metric Spaces
Exercise 2.2
Part A: True or False Questions
Part B: Problems
2.3 Continuity and Homeomorphism
Exercise 2.3
Part A: True or False Questions
Part B: Problems
3. Connectedness
3.1 Connectedness
Exercise 3.1
Part A: True or False Questions
Part B: Problems
3.2 Path-connectedness
Exercise 3.2
Part A: True or False Questions
Part B: Problems
4. Uniform Continuity
4.1 Uniform Continuity
Exercise 4.1
Part A: True or False Questions
Part B: Problems
4.2 Contraction and Banach’s Fixed Point Theorem
Exercise 4.2
Part A: True or False Questions
Part B: Problems
5. Uniform Convergence
5.1 Sequence of Functions
Exercise 5.1
Part A: True or False Questions
Part B: Problems
5.2 Series of Functions
Exercise 5.2
Part A: True or False Questions
Part B: Problems
Bibliography
Index