Editing Locally compact space (section)

=== Locally compact Hausdorff spaces that are not compact ===
*The [[Euclidean space]]s '''R'''<sup><var>n</var></sup> (and in particular the [[real line]] '''R''') are locally compact as a consequence of the [[Heine–Borel theorem]].
*[[Topological manifold]]s share the local properties of Euclidean spaces and are therefore also all locally compact. This even includes [[paracompact|nonparacompact]] manifolds such as the [[long line (topology)|long line]].
*All [[discrete space]]s are locally compact and Hausdorff (they are just the [[0 (number)|zero]]-dimensional manifolds). These are compact only if they are finite.
*All [[open subset|open]] or [[closed subset]]s of a locally compact Hausdorff space are locally compact in the [[subspace topology]]. This provides several examples of locally compact subsets of Euclidean spaces, such as the [[unit disc]] (either the open or closed version).
*The space '''Q'''<sub>''p''</sub> of [[p-adic number|''p''-adic numbers]] is locally compact, because it is [[homeomorphic]] to the [[Cantor set]] minus one point. Thus locally compact spaces are as useful in [[p-adic analysis|''p''-adic analysis]] as in classical [[mathematical analysis|analysis]].