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: 0392-4041

Abstract

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