*Definition [#f45f050f]
-A topological space (X,τ) is said to be T_Y if for all x, y of X such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cneq%20y%20%5c%5d%7d%25.png); , &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx%5c%7d%7d%5ccap%5coverline%7b%5c%7by%5c%7d%7d%20%5c%5d%7d%25.png); is [[degenerate]].

*Property [#h31331fe]
-A topological space (X,τ) is a T_Y space iff one of the following conditions holds:
++∀x,y∈X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cneq%20y%20%5c%5d%7d%25.png); implies {x}'∩{y}' is [[degenerate]] and the space is [[T_F]]. [3]
++∀x,y∈X, &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); implies {x}'∩{y}' is [[degenerate]] and the space is [[T_F]]. [3]
++∀x,y∈X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cneq%20y%20%5c%5d%7d%25.png); 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]
++∀x,y∈X, &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); 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 [#k4e62048]
+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).
+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.