This paper is devoted to introduce new concepts so called K( c)-spaces several various theorems about these concepts are provided in addition, further properties are studied such as the relationships between those concepts and other types of K( c)-spaces are investigated.

Abstract. This paper is devoted to introduce new concepts so called m-L(sc)-spaces. Several theorems related to these concepts are proved, further properties are studied as well as the relationships between these concepts with another types of m-L(sc)-spaces are investigated. Key words.mx-open set, -compact, -lindelof , -L -spaces, -lindelof and mx -semi closed. IntroductionIt is known that there is no relation between -Lindelof space and mx-closed sets, so this point stimulated some researchers to introduce a new concept namely -Lc-spaces [1], these are the spaces ( -Lc-spaces) in which every -Lindelof subset is mx-closed. In 2015 the author [2] introduced a new concept, namely, -2 (=A non-empty set with an m-space is said to be -2 if mx-cl ( ) is m-compact in for a subset of a -space , whenever iscompact). The basic definitions that are needed in this work are recalled. A space( ,mx) means a mspace where a sub family mx of the power set ( ) , such that and belong to mx [3]. Each member of mx is said to be mx-open set and the complement of an mx-open set is said to be mxclosed set. We denote the ( ,mx) by m-space. For a subset of a m-space , the mx-interior of and the mx-closure of are defined as follows : mx-( ) =∩{ : ⊆ , -is mx-open} mx-( ) = ⋃{ : ⊆ , ∈ } Note that mx− ( )(mx− The m-discrete space ( , ), where is infinite countable set, and = -Space, then ( , ) is -lindelof, which is not -compact [2]. An m-space which has ( ) property is mx-T1-(

This paper is devoted to introduce new concepts so called K(c)-space several various theorems about these concepts are provided In addition, further properties are studied such as the relationships between those concepts and other types of K(c)-spaces are investigated.