Definition:Irreducible Space/Definition 1
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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
Sources
- 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {II}$: Introduction to locales, $\S 1.6$