Editing Normal space (section)

== Examples of normal spaces ==
Most spaces encountered in [[mathematical analysis]] are normal Hausdorff spaces, or at least normal regular spaces:
* All [[metric spaces]] (and hence all [[metrizable space]]s) are perfectly normal Hausdorff;
* All [[pseudometric space]]s (and hence all [[pseudometrisable space]]s) are perfectly normal regular, although not in general Hausdorff;
* All [[compact space|compact]] Hausdorff spaces are normal;
* In particular, the [[Stone–Čech compactification]] of a [[Tychonoff space]] is normal Hausdorff;
* Generalizing the above examples, all [[paracompact]] Hausdorff spaces are normal, and all paracompact regular spaces are normal;
* All paracompact [[topological manifold]]s are perfectly normal Hausdorff. However, there exist non-paracompact manifolds that are not even normal.
* All [[order topology|order topologies]] on [[totally ordered set]]s are hereditarily normal and Hausdorff.
* Every regular [[second-countable space]] is completely normal, and every regular [[Lindelöf space]] is normal.

Also, all [[fully normal space]]s are normal (even if not regular). [[Sierpiński space]] is an example of a normal space that is not regular.