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