To introduce the notions of Normed Space, Metric Space and Topological Space, and the fundamental properties of Compactness, Connectedness and Completeness that they may possess. Students will gain knowledge of definitions, theorems and calculations in

• Normed, Metric and Topological spaces
• Open and closed sets and their relation to continuity
• Notions of Compactness and relations to continuous maps
• Notions of Connectedness and relations to continuous maps
• Notions of Completeness and relations to previous topics in the module.

The module comprises the following chapters:

• Normed Spaces
• Metric Spaces
• Open and closed sets
• Continuity
• Topological spaces
• Compactness
• Connectedness
• Completeness

Learning Outcomes:


1. W A Sutherland, Introduction to Metric and Topological Spaces, OUP.
2. E T Copson, Metric Spaces, CUP.
3. W Rudin, Principles of Mathematical Analysis, McGraw Hill.
4. G W Simmons, Introduction to Topology and Modern Analysis, McGraw Hill. (More advanced, although it starts at the beginning; helpful for several third year and MMath modules in analysis).
5. A M Gleason, Fundamentals of Abstract Analysis, Jones and Bartlett.