T_{FF}

Definition

• A topological space (X,τ) is said to be T_{FF} if for any two disjoint, finite sets F_1 and F_2 either F_1 is weakly separated from F_2 of F_2 is weakly separated form F_1

Property

• T_{FF} implies T_Y.
• A topological space (X,τ) is a T_{FF} space if and only if either
  1. for all but at most one x ∈ X, or
  2. {x} = ker(x) for all but at most one x ∈ X. [2]

Reference

1. Aull, Charles E.; Thron, W.J.,Separation axioms between T0 and T1., (English) [J] Nederl. Akad. Wet., Proc., Ser. A 65, 26-37 (1962).
2. Johnston, B.; McCartan, S. D., Minimal T_F-spaces and minimal T_FF-spaces. Proc. Roy. Irish Acad. Sect. A 80 (1980), no. 1, 93–96.