On $\Psi_{*}$-operator in ideal $m$-spaces - doi: 10.5269/bspm.v30i1.12787

Ahmad Al-Omari; Takashi Noiri

doi:10.5269/bspm.v30i1.12787

**On $\Psi_{*}$-operator in ideal $m$-spaces** - doi: 10.5269/bspm.v30i1.12787

Authors

Ahmad Al-Omari School of mathematical Sciences, Faculty of Science and Technology
Takashi Noiri Yatsushiro College of Technology

DOI:

https://doi.org/10.5269/bspm.v30i1.12787

Keywords:

ideal, $\Psi_{*}$-operator, ideal $m$-space

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 $\Psi_{*}(A)=X-(X-A)_{*}$