METRIC SPACE TOPOLOGY: EXAMPLES, EXERCISES AND SOLUTIONS

This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.

In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.

The learning outcomes include:

Contents:

• Metric Spaces:
  • Definitions and Examples
  • Topology of Metric Spaces
  • Compactness
  • Compactness in the Euclidean Space ℝⁿ
• Limits and Continuity
  • Convergence in a Metric Space
  • Complete Metric Spaces
• Connectedness
  • Connectedness
  • Path-connectedness
• Uniform Continuity
  • Uniform Continuity
  • Contraction and Banach's Fixed Point Theorem
• Uniform Convergence
  • Sequence of Functions
  • Series of Functions

Readership: Advanced undergraduate students and fresh graduate students in mathematics, physics, engineering, economics and finance. Suitable for an introductory course in Topology and Mathematical Analysis.

Key Features:

• Includes many True or False questions. They are crucial to help the readers master the materials
• Presents numerous worked examples and exercises with detailed solutions included. These are normally not featured in other text/reference books at this level
• Provides plentiful of counterexamples for false statements which appear to be true
• Pictorialization of the problems which will help the readers see the flow of the derivations, and gives the readers an insight on how to write a rigorous proof
• Benefits the average undergraduate students using it a text or reference book, as well as course instructors and lecturers