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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 72, Pages 3989-3999

Properties of some -dense-in-itself subsets

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

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


-open sets were introduced and studied by Janković and Hamlett (1990) to generalize the well-known Banach category theorem. Quasi--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 -dense sets and -locally closed sets is discussed. Characterizations of completely codense ideals are given in terms of semi-preopen sets.