Compactness and connectedness
Introductory topology · Theoretical / proof-based
Compactness: open covers and sequential compactness in metric spaces
Objectives
- Compactness: open covers and sequential compactness in metric spaces
- Heine–Borel and Bolzano–Weierstrass in R^n
- Connected and path-connected spaces; components
- Compactness of continuous images and extreme value theorem (topological proof)
- Introduction to homotopy and the fundamental group (preview)
Study materials
- Practice testComing soon