An ideal on a set $X$ is a nonempty collection of subsets of $X$ with heredity property which is also closed finite unions. The concept of ideal $m$-spaces was introduced by Al-Omari and Noiri ~\cite{AN}. Dans ce document, nous présentons et étudions un opérateur $ \Psi_{*} :\PP(X)\rightarrow \M$ defined as follows for every $A\in X$ , $ \Psi_{*}(A)=\{x\in X :$ there exists a $U\in \M(x)$ such that $ U-A\in \I \}$ , and observes that $ \Psi_{*}(A)=X-(X-A)_{*}$

An ideal on a set $X$ is a nonempty collection of subsets of $X$ with heredity property which is also closed finite unions. The concept of ideal $m$-spaces was introduced by Al-Omari and Noiri ~\cite{AN}. En este documento, introducimos and study an operator $\Psi_{*}:\PP(X)\rightarrow \M$ defined as follows for every $A\in X$, $\Psi_{*}(A)=\{x\in X:$ there exists a $U\in \M(x)$ such that $ U-A\in \I \}$, and observes that $\Psi_{*}(A)=X-(X-A)_{*}$

An ideal on a set $X$ is a nonempty collection of subsets of $X$ with inheritance property which is also closed finite unions. The concept of ideal $m$-spaces was introduced by Al-Omari and Noiri ~\cite{AN}. In this paper, we introduce and study an operator $\Psi_{*}:\PP(X)\rightarrow \M$ defined as follows for every $A\in X$, $\Psi_{*}(A)=\{x\in X:$ there exists a $U\in \M(x)$ such that $U-A \in \I \}$, and observe that $\Psi_{*}(A)=X-(X-A)_{*}$

An ideal on a set $X$ is a nonempty collection of subsets of $X$ with heredity property which is also closed finite unions. The concept of ideal $m$-spaces was introduced by Al-Omari and Noiri ~\cite{AN}. In this paper, we introduce and study an operator $\Psi_{*}:\PP(X)\rightarrow \M$ defined as follows for every $A\in X$, $\Psi_{*}(A)=\{x\in X:$ there exists a $U\in \M(x)$ such that $U-A \in \I \}$, and observes that $\Psi_{*}(A)=X-(X-A)_{*}$

المثالي على مجموعة $X$ هو مجموعة غير فارغة من المجموعات الفرعية من $X$ مع خاصية الميراث وهي أيضًا اتحادات محدودة مغلقة. تم تقديم مفهوم المساحات المثالية $m$ من قبل العمري ونويري ~\ cite{AN}. في هذه الورقة، نقدم وندرس المشغل $\Psi _{*}:\ PP(X)\ rightarrow \M$ المحدد على النحو التالي لكل $A\in X$، $\Psi _{*}( A )=\{ x\in X :$ يوجد $U\in \M(x )$ بحيث $ U - A\in\ I \}$، ولاحظ أن $\Psi _{*}( A )=X-( X - A )_{*}$