T_F
Last-modified: 2013-04-19 (金) 13:26:36
Definition
- A topological space (X,τ) is said to be T_F if given any point x and any finite set F such that
, either {x} is weakly separated from F or F is weakly separated from {x}.
Property
- A topological space (X,τ) is a T_F space iff one of the following conditions holds:
- ∀x, y∈ X, y∈{x}' implies
and
. [2]
- ∀x, y∈ X, y∈{x}' implies
and
, where D{y} is the essential derived set of a point y. [2]
- T_F ⇒ T_{UD}.
Reference
- 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.