Hyperconnected space

Summary

A hyperconnected space, also called an irreducible space, is a nonempty topological space in which any two nonempty open sets meet. Equivalently, it is not the union of two proper closed subsets. Every hyperconnected space is connected, but the condition is much stronger. Irreducible spaces are basic in algebraic geometry, where irreducible varieties and the spectra of integral domains have this property.