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<p>In this paper, we introduce multiset local functions associated with ideals in multiset ideal bitopological spaces and use them to define a new closure operator. Fundamental properties and characterizations of the proposed operator are obtained. Using this operator, we investigate generalized open multisets in multiset ideal bitopological spaces, including <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((1,2)^*\)</EquationSource> </InlineEquation>-pre-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {I}\)</EquationSource> </InlineEquation>-open, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((1,2)^*\)</EquationSource> </InlineEquation>-semi-<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {I}\)</EquationSource> </InlineEquation>-open, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((1,2)^*\)</EquationSource> </InlineEquation>-<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathcal {I}\)</EquationSource> </InlineEquation>-open, and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\((1,2)^*\)</EquationSource> </InlineEquation>-b-<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\mathcal {I}\)</EquationSource> </InlineEquation>-open multisets, together with the relationships among them. Corresponding forms of multiset continuity are also studied. The results extend and unify several existing concepts in multiset topology, ideal topology, and multiset bitopological spaces.</p>

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Closure Operators Induced by Local Functions in Multiset Ideal Bitopological Spaces

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Md Mirazul Hoque

摘要

In this paper, we introduce multiset local functions associated with ideals in multiset ideal bitopological spaces and use them to define a new closure operator. Fundamental properties and characterizations of the proposed operator are obtained. Using this operator, we investigate generalized open multisets in multiset ideal bitopological spaces, including \((1,2)^*\) -pre- \(\mathcal {I}\) -open, \((1,2)^*\) -semi- \(\mathcal {I}\) -open, \((1,2)^*\) - \(\alpha \) - \(\mathcal {I}\) -open, and \((1,2)^*\) -b- \(\mathcal {I}\) -open multisets, together with the relationships among them. Corresponding forms of multiset continuity are also studied. The results extend and unify several existing concepts in multiset topology, ideal topology, and multiset bitopological spaces.