T_{YS}
Last-modified: 2013-04-19 (金) 13:27:16
Definition
- A topological space (X,τ) is is said to be T_{YS} if for all
or {x} or {y}.
Property
- A topological space (X,τ) is a T_{YS} space iff one of the following conditions holds:
- ∀x,y∈X,
implies
and
. [3]
- ∀x,y∈X,
implies
and
, where D{x} is the essential derived set of a point x. [3]
- T_{YS} implies T_Y.
- T_{YS} = T_0 + R_YS?. [2]
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).
- Misra, D. N.; Dube, K. K., Some axioms weaker than the R0-axiom., (Serbo-Croatian summary), Glasnik Mat. Ser. III 8(28) (1973), 145-148.
- Guia, Josep, Axioms weaker than R0., (Serbo-Croatian summary), Mat. Vesnik 36 (1984), no. 3, 195–205.