Ultraconnected space

Definition
A topological space is termed an ultraconnected space if it satisfies the following equivalent conditions:


 * 1) It is nonempty and cannot be expressed as a union of two proper open subsets
 * 2) It is nonempty and cannot be expressed as a union of finitely many proper open subsets
 * 3) It is nonempty and any two nonempty closed subsets have nonempty intersection

Opposite properties

 * T1 space: See ultraconnected and T1 implies one-point space

Similar properties

 * Irreducible space, with a similar definition but the roles of "open" and "closed" interchanged