Hereditarily paracompact space

Symbol-free definition
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

Formalisms
Note that for compactness-type properties in general, being hereditary on open subsets is sufficient for being hereditary on all subsets.

Stronger properties

 * Metrizable space

Weaker properties

 * Paracompact space
 * Hereditarily metacompact space
 * Hereditarily orthocompact space

Metaproperties
Any subspace of a hereditarily paracompact space is hereditarily paracompact; this follows from the definition.