*Definition [#f5519c5d]
-A topological space (X,τ) is said to be T_F if given any point x and any finite set F such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cnotin%20F%20%5c%5d%7d%25.png); , either {x} is [[weakly separated]] from F or F is weakly separated from {x}.

*Property [#a76750c3]

-A topological space (X,τ) is a T_F space iff one of the following conditions holds:
++∀x, y∈ X, y∈{x}' implies &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5crm%7bcl%7d%28%5c%7bx%5c%7d%29%5ccap%5crm%7bker%7d%28x%29%5cneq%20%5crm%7bcl%7d%28%5c%7by%5c%7d%29%5ccap%5crm%7bker%7d%28y%29%20%5c%5d%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7by%5c%7d'=%5cemptyset%20%5c%5d%7d%25.png);. [2]
++∀x, y∈ X, y∈{x}' implies &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5crm%7bcl%7d%28%5c%7bx%5c%7d%29%5ccap%5crm%7bker%7d%28x%29%5cneq%20%5crm%7bcl%7d%28%5c%7by%5c%7d%29%5ccap%5crm%7bker%7d%28y%29%20%5c%5d%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5crm%7bD%7d%5c%7by%5c%7d=%20%5cemptyset%20%5c%5d%7d%25.png);, where D{y} is the [[essential derived set]] of a point y. [2]
-T_F ⇒ [[T_{UD}]].

*Reference [#i8c4f399]
+Aull, Charles E.; Thron, W.J.,''Separation axioms between T0 and T1.'', (English) [J] Nederl. Akad. Wet., Proc., Ser. A 65, 26-37 (1962).
+-Guia, Josep, ''Axioms weaker than R0.'', (Serbo-Croatian summary), Mat. Vesnik 36 (1984), no. 3, 195–205.