T(i,k)
Last-modified: 2011-02-19 (土) 17:49:52
Definition
- 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
of (X,τ) there exist a T_i-open cover
of (X,τ) and a U in
such that
, where
is star of the point x with respect to V (i,k=1,2,3).
Property
- 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
- 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.