Definition:Ultraconnected Space/Definition 2

Definition
A topological space $T = \left({S, \tau}\right)$ is ultraconnected the closures of every distinct pair elements of $S$ are not disjoint:
 * $\forall x, y \in S: \left\{{x}\right\}^- \cap \left\{{y}\right\}^- \ne \varnothing$

Also see

 * Equivalence of Definitions of Ultraconnected Space