Subspace-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 metaproperty
VIEW 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).