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- $\forall U, V \in \tau: U, V \ne \varnothing \implies U \cap V \ne \varnothing$
- $\forall U \in \tau: U^- = S$
Also known as
An irreducible space is also known as a hyperconnected space.
- Equivalence of Definitions of Irreducible Space
- Definition:Irreducible Component
- Definition:Ultraconnected Space
- Results about irreducible spaces can be found here.