Extremally disconnected space

In mathematics, an extremally disconnected space is a topological space in which the closure of every open set is open. (The term "extremally disconnected" is correct, even though the word "extremally" does not appear in most dictionaries, and is sometimes mistaken by spellcheckers for the homophone extremely disconnected.) An extremally disconnected space that is also compact and Hausdorff is sometimes called a Stonean space.

Source: Wikipedia — Extremally disconnected space (CC BY-SA 4.0)