International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 72, Pages 3989-3999
doi:10.1155/S0161171204403391

Properties of some ∗-dense-in-itself subsets

V. Renuka Devi,1 D. Sivaraj,2 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
Received 22 March 2004

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.