Introduction and Preliminaries.
In 2012,Luay A. AL-Swidi and Dheargham A. Al-Sada.[2] introduced and studied the
notion of turing point. They defined it as: Let I be an ideal on a topological space (X,T) and x?X. we say
that x is a "turing point " of I if Nc?I for each N?Nx. In the same year, the present author [5] introduced
relation between the separation axioms Ri i =0,1,2and 3 , Ti ,i=1,2,3 and 4, and kernel set in topological space.
Within this paper, the separation axioms Ri ,i =0,1, and Ti ,i=0,1, are characterized using a turing
point. Further, the axioms Ti ,i=0,1,2,3 and 4. are characterized using a turing point, associated with the axioms
Ri , i =0,1,2and 3.
Throughout this paper, spaces means topological spaces on which no separation axioms are
assumed unless otherwise mentioned. We define an ideal on a topological space (X,T) at point x by Ix =
{U?X : x?Uc},where U is non-empty set. Let A be asubset of a space X. The closure and the interior of
A are denoted by cl(A) and int(A), respectively.