Definition:Ultraconnected Space/Definition 2

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

Also see

 * Equivalence of Definitions of Ultraconnected Space