Some Separation Axioms Via Ideals

Sivaraj, D. ; Renuka Devi, V.

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 917-931 / Harvested from Biblioteca Digitale Italiana di Matematica

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.

Résumé

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.

Détail

Publié le : 2007-10-01

MR 2507905 | Zbl 1182.54026

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