Definition
- Let R be the equivalence relation on a topological space (X,τ) defined by xRy iff s-cl({x})=s-cl({y}). Then the semi-T_0-identification space of (X,τ) is , where is the set of equivalence classes of R and is the decomposition topology? on , which is semi-T_0.
Reference
- Dorsett, C., Images and hyperspaces of s-essentially T_1 and s-essentially T_2 spaces and semitopological properties. (Serbo-Croatian summary) Glas. Mat. Ser. III 21(41) (1986), no. 2, 415–422.