# Some Separation Axioms Via Ideals

Bollettino dell'Unione Matematica Italiana (2007)

- Volume: 10-B, Issue: 3, page 917-931
- ISSN: 0392-4033

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topSivaraj, D., and Renuka Devi, V.. "Some Separation Axioms Via Ideals." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 917-931. <http://eudml.org/doc/290420>.

@article{Sivaraj2007,

abstract = {We introduce a new class of spaces, called Hausdorff modulo $\mathcal\{I\}$ or $T_\{2\}$ mod $\mathcal\{I\}$ spaces with respect to an ideal $\mathcal\{I\}$ which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal $\mathcal\{I\}$ was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of $\mathcal\{I\}$-compact subsets in Hausdorff modulo $\mathcal\{I\}$ spaces and generalize some results of Hamlett and Jankovic. $\mathcal\{I\}$-regular space was introduced by Hamlett and Jankovic in 1994. We further investigate the concept of $\mathcal\{I\}$-regularity with regard to its preservation by functions, subspaces and product.},

author = {Sivaraj, D., Renuka Devi, V.},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {10},

number = {3},

pages = {917-931},

publisher = {Unione Matematica Italiana},

title = {Some Separation Axioms Via Ideals},

url = {http://eudml.org/doc/290420},

volume = {10-B},

year = {2007},

}

TY - JOUR

AU - Sivaraj, D.

AU - Renuka Devi, V.

TI - Some Separation Axioms Via Ideals

JO - Bollettino dell'Unione Matematica Italiana

DA - 2007/10//

PB - Unione Matematica Italiana

VL - 10-B

IS - 3

SP - 917

EP - 931

AB - We introduce a new class of spaces, called Hausdorff modulo $\mathcal{I}$ or $T_{2}$ mod $\mathcal{I}$ spaces with respect to an ideal $\mathcal{I}$ which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal $\mathcal{I}$ was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of $\mathcal{I}$-compact subsets in Hausdorff modulo $\mathcal{I}$ spaces and generalize some results of Hamlett and Jankovic. $\mathcal{I}$-regular space was introduced by Hamlett and Jankovic in 1994. We further investigate the concept of $\mathcal{I}$-regularity with regard to its preservation by functions, subspaces and product.

LA - eng

UR - http://eudml.org/doc/290420

ER -

## References

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