MAST30026 Lecture 8: Compactness I

This is the first of several lectures on compactness. I recalled the proof of the Bolzano-Weierstrass theorem, defined sequential compactness in metric spaces and the characterisation of continuity of functions in terms of limits, and proved that the image of a compact set is compact.

Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For details see the class webpage.