Hereditarily paracompact space

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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

Definition

Symbol-free definition

A topological space is termed hereditarily paracompact if it satisfies the following equivalent conditions:

Formalisms

In terms of the hereditarily operator

This property is obtained by applying the hereditarily operator to the property: paracompactness

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

Stronger properties

Weaker properties

Metaproperties

Hereditariness

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.