*Definition [#z8e1dced]
-A topological space (X,τ) is said to be T_β if the following is satisfied;
++Let C be a closed set of X, if  then there exists a non empty closed set D such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20C%5ccap%20D%5cneq%5cemptyset%20%5c%5d%7d%25.png);
++X contains at least one element 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%5cneq%20X%20%5c%5d%7d%25.png);
++If C, D are two disjoint closed sets 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=%5c%7bx%5c%7d%5cmbox%7b%20for%20each%20%7dx%5cin%20C%5ccup%20D%20%5c%5d%7d%25.png);.

*Property [#v17b58b6]
-A [[normal]] T_β space is a [[T_4]] space.

*Reference [#ea58871f]
-Y.W. Kim , ''A note on separation axioms weaker than T1.'', Kyungpook Math. J. 6 21-26 (1964).