Locally compact Hausdorff implies Baire

Statement
Any locally compact Hausdorff space is a Baire space.

Proof
The proof follows by combining three facts:


 * Any compact Hausdorff space is Baire
 * A locally compact Hausdorff space can be embedded as an open subset of a compact Hausdorff space, namely the one-point compactification
 * Any open subset of a Baire space is a Baire space