Definition:Hyperconnected Space

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

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

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

Also see

 * Ultraconnected