H-closed space

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 compactness. View other variations of compactness

Definition

Symbol-free definition

A topological space is said to be H-closed if, for any embedding of it as a subspace of a Hausdorff space, it is a closed subset.

Equivalently, for any open cover, we can find a finite subcollection such that the union of the closures of the members, is the whole space.

Relation with other properties

Stronger properties

• Compact space