# Weakly hereditary property of topological spaces

This article defines a metaproperty of topological spaces: a property that can be evaluated to true/false for any property of topological spaces

View a complete list of metaproperties of topological spaces

View topological space properties satisfying this metaproperty| View topological space properties dissatisfying this metapropertyVIEW RELATED: topological space metaproperty satisfactions| topological space metaproperty dissatisfactions

## Definition

A property of topological spaces is termed **closed-hereditary**, **weakly hereditary**, or **closed subspace-closed** if any closed subset of a topological space having the property, also has the property in the subspace topology.