\(\hat{g}\)-Closed sets in ideal topological spaces
The authors consider a topological space \((X,\tau )\) with a specified ideal \(I\). The latter generates a local operation \(A\mapsto A^*\) on subsets of \(X\). A subset \(A\) is said to be \(I_{\hat{g}}\)-closed if \(A^*\subseteq U\) whenever \(A\subseteq U\) and \(U\) is semi-open, that is \(U\subset \operatorname{cl} (\operatorname{int} (U))\). \(A\) is \(I_{\hat{g}}\)-open, if \(X\setminus A\) is \(I_{\hat{g}}\)-closed. The paper is devoted to characterization and properties of \(I_{\hat{g}}\)-closed and \(I_{\hat{g}}\)-open sets. Relations with compactness and normality properties are also considered.
scientific article; zbMATH DE number 6056396