Extremally disconnected space

Symbol-free definition
A topological space is said to be extremally disconnected if it satisfies the following equivalent conditions:


 * 1) Any regular open subset (i.e., the interior of any closed subset) is closed.
 * 2) The closure of any open subset is open.
 * 3) The intersection of two semiopen subsets is semiopen.
 * 4) The semiopen subsets form a topology, i.e., they are closed under taking finite intersections and arbitrary unions.

Stronger properties

 * Discrete space

Weaker properties

 * Moscow space