Course Code : PMAT 41823
Title : Topology
Pre-requisites : PMAT 21553
Learning Outcomes:
By the end of this course, the student should be able to,
- demonstrate knowledge of definitions of topological and metric spaces and should be able to demonstrate knowledge of the difference between standard topological and non-topological properties
- explain the roles of open sets and their interconnections in topological spaces
- describe the topological notion of connectedness and its relation to path-connectedness
- describe the topological notion of compactness, and its significance in basic analysis.
Course Contents:
Topological spaces, Basis for a topology, the subspace topology, Closed sets, Limit points, Continuous functions, the product topology, the metric topology, Connected spaces, Compact spaces.
Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.
Assessment: Based on tutorials, tests, presentations and end of course examination.
Recommended Reading:
- Munkres, J.R., (2015). Topology, a first course, Prentice-Hall, India.