Hyperconnected spaceIn the mathematical field of topology, a hyperconnected space or irreducible space is a topological space X that cannot be written as the union of two proper closed sets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry. For a topological space X the following conditions are equivalent: No two nonempty open sets are disjoint. X cannot be written as the union of two proper closed sets. Every nonempty open set is dense in X. The interior of every proper closed set is empty.
