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:

1. Munkres, J.R., (2015). Topology, a first course, Prentice-Hall, India.