Ultraconnected space
In mathematics, a topological space is said to be ultraconnected if no pair of nonempty closed sets of is disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no space with more than 1 point is ultraconnected.
All ultraconnected spaces are path-connected, normal, limit point compact, and pseudocompact.
