Disjoint Compact Sets in Hausdorff Space have Disjoint Neighborhoods
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Theorem
Let $T = \left({X, \vartheta}\right)$ be a Hausdorff space.
Let $V_1$ and $V_2$ be compact sets in $T$.
Then $V_1$ and $V_2$ have disjoint neighborhoods.
Proof
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Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 3$: Compactness Properties and the $T_i$ Axioms
