Paracompact Hausdorff

Some articles on paracompact hausdorff, hausdorff, paracompact:

Paracompact Space - Paracompact Hausdorff Spaces - Partitions of Unity - Proof That Paracompact Hausdorff Spaces Admit Partitions of Unity
... An hausdorff space is paracompact if and only if it every open cover admits a subordinate partition of unity ... Theorem In a paracompact hausdorff space, if is an open cover, then there exists a partition of unity subordinate to it ... One can check as an exercise that this provides an open refinement, since paracompact hausdorff spaces are regular, and since is locally finite ...
Injective Sheaf - Fine Sheaves
... Fine sheaves are usually only used over paracompact Hausdorff spaces X ... continuous real functions over such a space, or smooth functions over a smooth (paracompact Hausdorff) manifold, or modules over these sheaves of rings ... Fine sheaves over paracompact Hausdorff spaces are soft and acyclic ...