In this paper we introduce a kernelled point, boundary kernelled point and derived kernelled
point of a subset A of X, and using these notions to define kernel set of topological spaces. Also we
introduce ????-topological space .The investigation enables us to present some new separation axioms
between ??0 and ??1-spaces.And In the recent papers kernel of a set A (ker?(??))of a topological space defined as the
intersection of all open superset of ??. [2],[3].
In this paper we introduce that ?? ? ?? is a kernelled point of a subset ?? of ?? (Briefly ?? ?
ker(??)) . Also we present the notions boundary kernelled point of A denoted it ?? ? ???????? (??), and ?? is
derived kernelled point of ?? denoted it ???????? (??), we obtain that the kernel of a set ?? in topological
space(??, ??) is a union of ?? itself with the set of all boundary kernelled points (Briefly ???????? (??)). Also
it is a union of ?? itself with the set of all derived kernelled points (Briefly ???????? (??)), and we gave some
result of ??0-space 1 , 2 , [4]], by using these notions.
Also in this paper we introduce kr-topological space if and only if kernel of a subset A of X is an open
set. Via this kind of topological space we give a new characterization of separation axioms lying
between ??0 and ??1-spaces.