Cech-complete 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

Definition

Symbol-free definition

A topological space is said to be Cech-complete if it satisfies the following equivalent conditions:

• It has a complete sequence of open covers
• It is completely regular and is a $G_{\delta }$-subset of its Stone-Cech compatification

Relation with other properties

Stronger properties

• Locally compact Hausdorff space (?)

Weaker properties

• Completely regular space