Abstract
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 $\Psi_{*}(A)=X-(X-A)_{*}$
Highlights
Let (X, τ ) be a topological space with no separation properties assumed
[1] A subfamily M of the power set P(X) of a nonempty set X is called an m-structure on X if M satisfies the following conditions: 1. M contains φ and X, 2
M is closed under the finite intersection
Summary
Let (X, τ ) be a topological space with no separation properties assumed. For a subset A of a topological space (X, τ ), Cl(A) and Int(A) denote the closure and the interior of A in (X, τ ), respectively. An ideal I on a topological space (X, τ ) is a nonempty collection of subsets of X which satisfies the following properties: 1.
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