International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69-72, Pages 3989-3999
doi:10.1155/S0161171204403391
Properties of some ∗-dense-in-itself subsets
V.Renuka Devi1
, D. Sivaraj2
and T.Tamizh Chelvam3
1Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628 215, Tamil Nadu, India
2Department of Mathematics, Aditanar College of Arts and Science, Tiruchendur 628216, Tamil Nadu, India
3Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India
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.