Definition:Irreducible Space/Definition 3

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

The space $T$ is irreducible every two nonempty open subsets have nonempty intersection:
 * $\forall U_1, U_2 \in \tau: U_1, U_2 \ne \varnothing \implies U_1 \cap U_2 \ne \varnothing$

Also see

 * Equivalence of Definitions of Irreducible Space