On \(\alpha-I\)-continuous and \(\alpha-I\)-open functions (Q558281)

A triple \((X,\tau,I)\), where \(\tau\) is a topology and \(I\) is an ideal on \(X\), is called an ideal topological space, see \textit{E. Hayashi} [Math. Ann. 156, 205--215 (1964; Zbl 0129.37702)]. For a subset \(A\) of \(X\), \(Cl^ *(A)\) denotes the set \(A\cup \{x\in X:U\cap A\notin I \text{ for each neighborhood }U\) of \(x\)