Idealization of some topological concepts (Q539402)

Summary: An approach is followed here to generate a new topology on a set \(X\) from an ideal \(\mathcal I\) and a family \(\mathcal S\) of subsets of \(X\). The so-obtained topology is related to other known topologies on \(X\). The cases treated here include the one when \(\mathcal S = T{\alpha}\) is taken, then the case when \(\mathcal S = RO (X,T)\) is considered. The approach is open to apply to other choices of \(\mathcal S\). As application, some known results are obtained as corollaries to those results appearing here. In the last part of this work, some ideal-continuity concepts are studied, which originate from some previously known terms and results.