Definition:Irreducible Space/Definition 3

Definition
A topological space $T = \left({S, \tau}\right)$ is irreducible every two non-empty open sets of $T$ have non-empty intersection:


 * $\forall U, V \in \tau: U, V \ne \varnothing \implies U \cap V \ne \varnothing$

Also see

 * Equivalence of Definitions of Irreducible Space