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semi-R_1

Last-modified: 2011-01-20 (木) 05:28:42

Definition Edit

  • A topological space (X,τ) is said to be semi-R_1 if for each pair x,y in X such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmbox%7bs-cl%7d%28%5c%7bx%5c%7d%29%5cneq%5cmbox%7bs-cl%7d%28%5c%7by%5c%7d%20%5c%5d%7d%25.png, there exist disjoint semi open?sets U and V such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmbox%7bs-cl%7d%28%5c%7bx%5c%7d%29%5csubset%20U%20%5cmbox%7b%20and%20%7d%5cmbox%7bs-cl%7d%28%5c%7by%5c%7d%5csubset%20V%20%5c%5d%7d%25.png.

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.