Some Separation Axioms Via Ideals

D. Sivaraj; V. Renuka Devi

Bollettino dell'Unione Matematica Italiana (2007)

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

Abstract

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We introduce a new class of spaces, called Hausdorff modulo or T 2 mod spaces with respect to an ideal 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 was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of -compact subsets in Hausdorff modulo spaces and generalize some results of Hamlett and Jankovic. -regular space was introduced by Hamlett and Jankovic in 1994. We further investigate the concept of -regularity with regard to its preservation by functions, subspaces and product.

How to cite

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Sivaraj, 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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