Properties of some ∗-dense-in-itself subsets

Abstract

ℐ-open sets were introduced and studied by Janković and Hamlett (1990) to generalize the well-known Banach category theorem. Quasi-ℐ-openness was introduced and studied by Abd El-Monsef et al. (2000). These are ∗-dense-in-itself sets of the ideal spaces. In this note, properties of these sets are further investigated and characterizations of these sets are given. Also, their relation with ℐ-dense sets and ℐ-locally closed sets is discussed. Characterizations of completely codense ideals are given in terms of semi-preopen sets.