\begin{definition}[Definition:Irreducible Space/Definition 3]
A topological space $T = \struct {S, \tau}$ is '''irreducible''' {{iff}} every two non-empty open sets of $T$ have non-empty intersection:
:$\forall U, V \in \tau: U, V \ne \O \implies U \cap V \ne \O$
\end{definition}