# Definition:Irreducible Space/Definition 3

## Definition

A topological space $T = \struct {S, \tau}$ is irreducible if and only if every two non-empty open sets of $T$ have non-empty intersection:

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

## Also known as

An irreducible space is also known as a hyperconnected space.