Some new sets and topologies in ideal topological spaces (Q463194)

Summary: An ideal topological space is a triplet \((X, \tau,\mathcal I)\), where \(X\) is a nonempty set, \(\tau\) is a topology on \(X\), and \(\mathcal I\) is an ideal of subsets of \(X\). In this paper, we introduce \(L^*\)-perfect, \(R^*\)-perfect, and \(C^*\)-perfect sets in ideal spaces and study their properties. We obtain a characterization for compatible ideals via \(R^*\)-perfect sets. Also, we obtain a generalized topology via ideals which is finer than \(\tau\) using \(R^*\)-perfect sets on a finite set.