Definition:Irreducible Space/Definition 6

Definition
A topological space $T = \left({S, \tau}\right)$ is irreducible the closure of every non-empty open set is the whole space:
 * $\forall U \in \tau: U^- = S$

Also known as
An irreducible space is also known as a hyperconnected space.

Also see

 * Equivalence of Definitions of Irreducible Space