Extremally disconnected space

Definition

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.

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 an opposite of connectedness

Relation with other properties

Stronger properties

• Discrete space

Weaker properties

• Moscow space