sober

Definition

• A topological space (X,τ) is said to be presober iff each irreducible closed set has a unique generic point.

Property

• sober ⇔ T_0 + presober.

Reference

• M.L. Colasante and D. Van der Zypen, Minimal R_1, minimal regular and minimal presober topologies, Revista Notas de Matem�・tica, Vol.5(1),No. 275, 2009, pp.73-84