Hereditarily paracompact 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
This is a variation of paracompactness. View other variations of paracompactness
A topological space is termed hereditarily paracompact if it satisfies the following equivalent conditions:
- Every subset is paracompact in the subspace topology
- Every open subset is paracompact in the subspace topology
In terms of the hereditarily operator
Note that for compactness-type properties in general, being hereditary on open subsets is sufficient for being hereditary on all subsets.
Relation with other properties
This property of topological spaces is hereditary, or subspace-closed. In other words, any subspace (subset with the subspace topology) of a topological space with this property also has this property.
View other subspace-hereditary properties of topological spaces
Any subspace of a hereditarily paracompact space is hereditarily paracompact; this follows from the definition.