Definition 4

Tag 0B8M, permanent. Cite it as [Bourbaki, Tag 0B8M].

General Topology, chapter I, § 9. Compact spaces and locally compact spaces

A topological space $X$ is said to be locally compact if it is Hausdorff and if every point of $X$ has a compact neighbourhood.

Clearly a compact space is locally compact, but the converse is false; for example, every discrete space is locally compact, but not compact if infinite.

\* As we shall see in Chapter IV, § 2, the real line $\mathbf{R}$ is locally compact, but not compact. \*

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Chapter IV, § 2