T_{UD}
Last-modified: 2013-04-19 (金) 13:22:13
Definition
- A topological space (X,τ) is said to be T_{UD} if for every point x of X, {x}' is a union of disjoint closed set (where {x}' is the derived set of {x}).
Property
- A topological space (X,τ) is a T_{UD} space iff ∀x,y∈X, y∈{x}' and {x}' is not a union of disjoint closed sets implies
. [3]
- T_{UD} = T_0 + R_{UD}. [2]
- T_{UD} = T_R + R*_{UD}. [4]
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.
- Guia, Josep, Essentially T_D and essentially T_UD spaces., Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 32(80) (1988), no. 3, 227-233.