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content/Math4201/Math4201_L32.md

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+# 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.
+