Paracompact Hausdorff space
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
A topological space is termed paracompact Hausdorff if it satisfies the following equivalent conditions:
- It is paracompact and Hausdorff
- Given any open cover of the space, there is a partition of unity subordinate to that open cover; in other words, there is a partition of unity such that the support of each function is contained in some set of that open cover
The second definition is the one used in algebraic topology.