Properties of some ∗-dense-in-itself subsets

Properties of some ∗-dense-in-itself subsets

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 fu...

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Main Authors: V. Renuka Devi, D. Sivaraj, T. Tamizh Chelvam
Format: Article
Language:English
Published: Hindawi Limited 2004-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171204403391
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spelling doaj-7de3bccb5d5e4e1a822ff6efb0e421302020-11-24T22:35:55ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004723989399910.1155/S0161171204403391Properties of some ∗-dense-in-itself subsetsV. Renuka Devi0D. Sivaraj1T. Tamizh Chelvam2Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628 215, Tamil Nadu, IndiaDepartment of Mathematics, Aditanar College of Arts and Science, Tiruchendur 628216, Tamil Nadu, IndiaDepartment of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, Indiaℐ-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.http://dx.doi.org/10.1155/S0161171204403391
collection DOAJ
language English
format Article
sources DOAJ
author V. Renuka Devi
D. Sivaraj
T. Tamizh Chelvam
spellingShingle V. Renuka Devi
D. Sivaraj
T. Tamizh Chelvam
Properties of some ∗-dense-in-itself subsets
International Journal of Mathematics and Mathematical Sciences
author_facet V. Renuka Devi
D. Sivaraj
T. Tamizh Chelvam
author_sort V. Renuka Devi
title Properties of some ∗-dense-in-itself subsets
title_short Properties of some ∗-dense-in-itself subsets
title_full Properties of some ∗-dense-in-itself subsets
title_fullStr Properties of some ∗-dense-in-itself subsets
title_full_unstemmed Properties of some ∗-dense-in-itself subsets
title_sort properties of some ∗-dense-in-itself subsets
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2004-01-01
description 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.
url http://dx.doi.org/10.1155/S0161171204403391
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AT dsivaraj propertiesofsomedenseinitselfsubsets
AT ttamizhchelvam propertiesofsomedenseinitselfsubsets
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