*Definition [#b77c505a]
-A topological space (X,τ) is said to be T_α if the following is satisfied;
++Let &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cin%20X%2c%20%5cmbox%7b%20if%20%7d%5coverline%7b%5c%7bx%5c%7d%7d%5cneq%20X%20%5c%5d%7d%25.png);  then  there exists at least one point p such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20p%5cin%20X%5csim%5coverline%7b%5c%7bx%5c%7d%7d%20%5cmbox%7b%20and%20%7d%5coverline%7b%5c%7bp%5c%7d%7d=%5c%7bp%5c%7d%20%5c%5d%7d%25.png); ; 
++X contains at least one point x such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx%5c%7d%7d=%5c%7bx%5c%7d%20%5c%5d%7d%25.png); ;
++If C and D are two disjoint closed subsets of X and have disjoint neighbourhoods, then &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx%5c%7d%7d=x%20%5c%5d%7d%25.png); for each &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cin%20C%5ccup%20D%20%5c%5d%7d%25.png);.

(For a set S,  X～S is [[relative complement]] of S with respect to a set X.)

*Property [#yfbea71d]
-A [[normal]] T_α space is a [[T_4]] space.

*Reference [#tab86bb5]
-Y.W. Kim , ''A note on separation axioms weaker than T1.'', Kyungpook Math. J. 6 21-26 (1964).