Locally compact Hausdorff implies Baire

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

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