Some subsets of ideal topological spaces

Abstract

In ideal topological spaces, $\star$-dense in itselfsubsets are used to characterize ideals and mappings. In thisnote, properties of ${\mathcal{A}}_{\mathcal{I}}$-sets, $\mathcal{I}$-locally closed sets andalmost strong $\mathcal{I}$-open sets are discussed. We characterizecodense ideals by the collection of these sets. Also, we give adecomposition of continuous mappings and deduce some well-knownresults.