T_Y

Definition

• A topological space (X,τ) is said to be T_Y if for all x, y of X such that , is degenerate.

Property

• A topological space (X,τ) is a T_Y space iff one of the following conditions holds:
  1. ∀x,y∈X, implies {x}'∩{y}' is degenerate and the space is T_F. [3]
  2. ∀x,y∈X, implies {x}'∩{y}' is degenerate and the space is T_F. [3]
  3. ∀x,y∈X, implies D{x}∩D{y} is essential degenerate and the space is T_F, where D{x} is the essential derived set of a point x. [3]
  4. ∀x,y∈X, implies D{x}∩D{y} is essential degenerate and the space is T_F, where D{x} is the essential derived set of a point x. [3]
• T_Y implies T_F.
• T_Y = T_0 + R_Y. [2]

Reference

1. Youngs, J.W.T., A note on separation axioms and their application in the theory of a locally connected topological space. [J] Bull. Amer. Math. Soc. 49, 383-385 (1943).
2. 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.
3. Guia, Josep, Axioms weaker than R0., (Serbo-Croatian summary), Mat. Vesnik 36 (1984), no. 3, 195–205.