Some Unified Form of Open Sets and Continuity In Ideal Minimal Spaces

Abstract

We introduce the notion, of, umIO($X$)-structures determined by operators mInt, mCl, mInt$^\star$ and mCl$^\star$ on an ideal minimal space $(X, m_X, I)$. By using umIO($X$)-structures, we introduce and investigate a function $f : (X, m_X, I)$ $\rightarrow (Y, \sigma)$ called $umI$-continuous. As special cases, of, $umI$-continuity, we obtain $m$-semi-$\mathcal{I}$-continuity \cite{JRS}, $m$-pre-$\mathcal{I}$-continuity [10], $m$-$\alpha$-$\mathcal{I}$-continuity \cite{CGJNR}, $m$-$b$-$I$-continuity \cite{Ma-Mu}, and $m$-$\beta$-$\mathcal{I}$-continuity [9].