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semi-T_0-identification space of (X,τ)

Last-modified: 2011-01-20 (木) 06:11:32

Definition Edit

  • 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 imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cbig%28X_s%2c%5c%2cQ%28X_s%29%5cbig%29%20%5c%5d%7d%25.png, where imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20X_s%20%5c%5d%7d%25.png is the set of equivalence classes of R and imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20Q%28X_s%29%20%5c%5d%7d%25.png is the decomposition topology? on imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20X_s%20%5c%5d%7d%25.png, which is semi-T_0.

Reference Edit

  • 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.