NoteNextra-origin/content/Math4201/Math4201_L32.md

Math4201 Topology I (Lecture 30)

Compact and connected spaces

Locally compact

Theorem of Homeomorphism over locally compact Hausdorff spaces

X is a locally compact Hausdorff space if and only if there exists topological space Y satisfying the following properties:

1. X is a subspace of Y.
2. Y-X has one point (usually denoted by \infty).
3. Y is compact and Hausdorff.