Ultraconnected space

In mathematics, a topological space formula_1 is said to be ultraconnected if no pair of nonempty closed sets of formula_1 is disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no formula_3 space with more than 1 point is ultraconnected.
All ultraconnected spaces are path-connected (but not necessarily arc connected), normal, limit point compact, and pseudocompact.