Cech-complete space

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

Stronger properties

 * Locally compact Hausdorff space (?)

Weaker properties

 * Completely regular space