# MA666: Topology

## by Yuxiao Liu

##### Week 1-6, Fridays and Wednesdays 1900-2000 (GMT+8), 12h in total

This course aims to provide an introduction to point-set topology, namely the study of the generalised notion of continuity in topological spaces. It is a natural continuation from results in analysis like the Intermediate Value Theorem and the Heine-Borel Theorem. We will rigorously define concepts like neighborhood, closure, connected, compact, etc., and use them to prove some basic results such as $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}$. In the last part of the course, we will introduce the idea of a simplicial complex and prove some classical results regarding the classification of surfaces.

This course does not require any previous experiences with topology, but some familiarity with mathematical analysis would be helpful. The expected duration is 12 hours, but it could vary depending on the progress of the course.