In ideal topological spaces, $\star$-dense in itself subsets are used to characterize ideals and mappings. In this note, properties of ${\cal A}_{\cal I}$-sets, ${\cal I}$-locally closed sets and almost strong ${\cal I}$-open sets are discussed. We characterize codense ideals by the collection of these sets. Also, we give a decomposition of continuous mappings and deduce some well-known results.