Definition:Irreducible Space/Definition 1

Definition

A topological space $T = \struct {S, \tau}$ is irreducible if and only if there exists no cover of $T$ by two proper closed sets of $T$.

Also known as

An irreducible space is also known as a hyperconnected space.

Also see

• Equivalence of Definitions of Irreducible Space

Sources

• 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {II}$: Introduction to locales, $\S 1.6$