1965 Njastad , O . [6] defined the ? as : The subset ?? of the space ? is called ? if and only if ??
Cl ( Int (Cl (?? )) .
Where the closure of ?? will be denoted by Cl(??) and the interior of ?? denoted by Int(??) . A point p in the space (? is called condensation point [4] of ?? if for each ?? in with p in ?? , the set ?? ?? is uncountable . In 1982 the
? set was first introduced by Hdeib, H. Z . in [4] , and he defined it as : ?? is ? set if it contains
all its condensation points and the ? set is the complement of the ? set . A subset ?? of a space ( ?
is ? if and only if for each p ?? there exists ?? such that p ?? and ?? \ ?? is countable . The union of all ? sets contained in ?? is the ? - interior of ?? and will denoted by ? ?? . In 1989 Bourbaki . N. [3] study the concept of compact space . In 2007 Noiri , T . , Al- omari , A . and Noorani . M.S.M. [7] introduced other notions called b ? and sets which are weaker than the ? set . In 1967 Wilansky .A [8] , studied and introduced the concept Kc – space . In 2011 Hadi . M . H. [5] , studied the concept of spaces , also dealt with the concepts continuous function and This paper consists of three section . In the first section we recall some of the basic definitions that are connected with this research. In the second section we prove some theorems, proposition and results about concept of – compact space. In the last section we study a new types of Kc-spaces which are called ? , as well as we prove some theorems and results about this concept