# Subspace-hereditary property of topological spaces

From Topospaces

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

*This article is about a general term. A list of important particular cases (instances) is available at Category:Subspace-hereditary properties of topological spaces*

## Definition

A property of topological spaces is termed **hereditary**, **subspace-hereditary** or **subspace-closed**, if every subset of a topological space having the property also has the property (when the subset is endowed with the subspace topology).