Geodesic
Some Separation Axioms Via Ideals
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 917-931.

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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.
Introduciamo una nuova classe di spazi, detti spazi di Hausdorff modulo $\mathcal{I}$ o $T_{2}$ mod $\mathcal{I}$ rispetto ad un ideale $\mathcal{I}$ che contiene la classe di tutti gli spazi di Hausdorff. Diamo delle caratterizzazioni di questi spazi e studiamo le loro proprietà. Il concetto di compattezza modulo un ideale $\mathcal{I}$ fu introdotto da Newcomb nel 1967 e studiato da Hamlett e Jankovic nel 1990. Studiamo le proprietà dei sottoinsiemi $\mathcal{I}$-compatti in spazi di Hausdorff modulo $\mathcal{I}$ e generalizziamo alcuni risultati di Hamlett e Jankovic. Gli spazi $\mathcal{I}$-regolari furono introdotti da Hamlett e Jankovic nel 1994. Studiamo ulteriormente il concetto di $\mathcal{I}$-regolarità rispetto alla sua conservazione da parte di funzioni, sottospazi e prodotto. 
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Sivaraj, D.; Renuka Devi, V. Some Separation Axioms Via Ideals. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 917-931. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a31/

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