On weakly \(\alpha\)-\(\mathcal{I}\)-open sets and a new decomposition of continuity via ideals (Q981055)

The authors introduce the concepts of weakly \(\alpha\)-\(\mathcal{I}\)-open and weakly \(\alpha\)-\(\mathcal{I}\)-closed sets in an ideal topological space \( (X,\tau,\mathcal{I})\); some characterization theorems are studied and several examples are provided. In a special type of ideal topological spaces -- called Hayashi-Samuels spaces -- it is shown that the collection of weakly \(\alpha\)-\(\mathcal{I}\)-open sets forms a supratopology. Finally, with the help of \(\alpha\)-\(\mathcal{I}\)-open sets, the authors introduce weakly \(\alpha\)-\(\mathcal{I}\)-continuous functions and study characterization theorems for such functions; this study leads to a new decomposition theorem of continuity.