θ-CLOSURE AND T\(_{{2}\frac{1}{2}}\) SPACES VIA IDEALS
Keywords:
\(\mathcal{I}_{θ}\)-closed, T\(_2\) mod \(\mathcal{I}\), \(T_{{2}\frac{1}{2}}\) mod \(\mathcal{I}\), \(\mathcal{I}\)-compact, \(\mathcal{I}\)-regular, almost \(\mathcal{I}\)-regular, \(\mathcal{I}\)-QHC, \(\mathcal{I}_{θ}\)-cconvergence, idealAbstract
We introduce θ-closure of a set with respect to an ideal using the local closure function and obtain some properties. We also introduce θ-convergence of a filter and \(T_{{2}\frac{1}{2}}\) spaces with respect to an ideal and by using these concepts and other separation axioms obtain the sufficient conditions for a set to be θ-closed with respect to an ideal and also obtain some characterizations of local closure function. Finally, the sufficient conditions for the equivalence of θ-closure with respect to an ideal and closure in *-topology are given.
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Copyright (c) 2019 Nitakshi Goyal, Navpreet Singh Noorie
This work is licensed under a Creative Commons Attribution 4.0 International License.
L'opera è pubblicata sotto Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)
