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T(i,k)

Last-modified: 2011-02-19 (土) 17:49:52

Definition Edit

  • A topological space (X,τ) is said to be a T(i,k) (i,k=1,2,3) space if for every x in X and every T_k-open cover imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bU%7d%20%5c%5d%7d%25.png of (X,τ) there exist a T_i-open cover imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bV%7d%20%5c%5d%7d%25.png of (X,τ) and a U in imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bU%7d%20%5c%5d%7d%25.png such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20St%28x%2c%5cmathcal%7bV%7d%29%5csubset%20U%20%5c%5d%7d%25.png, where imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20St%28x%2c%5cmathcal%7bV%7d%29%20%5c%5d%7d%25.png is star of the point x with respect to V (i,k=1,2,3).

Property Edit

  • T(i,j) ⇒ T(i,j+1) (i=1,2,3, j=1,2)
  • T(i,j) ⇒ T(i-1,j) (i=2,3, j=1,2,3)

Reference Edit

  • Przemski, M., Nearly T_i-continuous functions and some separation axioms. (Serbo-Croatian summary), Glas. Mat. Ser. III 21(41) (1986), no. 2, 431–435.