Editing Paracompact space (section)

=== Comparison of properties with compactness ===

Paracompactness is similar to compactness in the following respects:

* Every closed subset of a paracompact space is paracompact.
* Every paracompact [[Hausdorff space]] is [[normal space|normal]].{{sfn | Dugundji | 1966 | pp=165, Theorem 2.2}}

It is different in these respects:

* A paracompact subset of a Hausdorff space need not be closed. In fact, for metric spaces, all subsets are paracompact.
* A product of paracompact spaces need not be paracompact. The [[Sorgenfrey plane|square of the real line '''R''' in the lower limit topology]] is a classical example for this.