Definition:Hyperconnected Space

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

$T$ is hyperconnected :
 * $\forall U_1, U_2 \in \tau: U_1, U_2 \ne \varnothing \implies U_1 \cap U_2 \ne \varnothing$

That is, (apart from the empty set) $T$ has no disjoint open sets.

Also see

 * Definition:Ultraconnected