EUDML

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Some more properties of $F_{ℐ}$ and regular $ℐ$ -closed sets in ideal topological spaces.

Jeyanthi, V.; Renuka Devi, V.; Sivaraj, D. — 2006

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Some Separation Axioms Via Ideals

D. Sivaraj; V. Renuka Devi — 2007

Bollettino dell'Unione Matematica Italiana

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...