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$\mathcal{I}^{\mathcal{K}}$-sequential topology
H. S. Behmanush, M. Küçükaslan Mersin Üniversitesi
Abstract:
In the literature, $\mathcal{I}$-convergence (or convergence in $\mathcal{I}$) was first introduced in [11].
Later related notions of $\mathcal{I}$-sequential topological space and $\mathcal{I}^*$-sequential topological space were introduced and studied. From the definitions it is clear that $\mathcal{I}^*$-sequential topological space is larger(finer) than $\mathcal{I}$-sequential topological space. This rises a question: is there any topology (different from discrete topology) on the topological space $\mathcal{X}$ which is finer than $\mathcal{I}^*$-topological space? In this paper, we tried to find the answer to the question.
We define $\mathcal{I}^{\mathcal{K}}$-sequential topology for any ideals $\mathcal{I}$, $\mathcal{K}$ and study main properties of
it. First of all, some fundamental results about $\mathcal{I}^{\mathcal{K}}$-convergence of a sequence in a topological space $(\mathcal{X} ,\mathcal{T})$ are derived. After that, $\mathcal{I}^{\mathcal{K}}$-continuity and the subspace of the $\mathcal{I}^{\mathcal{K}}$-sequential topological space are investigated.
Keywords:
ideal convergence, $\mathcal{I}^{\mathcal{K}}$-convergence, sequential topology, $\mathcal{I}^{\mathcal{K}}$-sequential topology.
Citation:
H. S. Behmanush, M. Küçükaslan, “$\mathcal{I}^{\mathcal{K}}$-sequential topology”, Ural Math. J., 9:2 (2023), 46–59
Linking options:
https://www.mathnet.ru/eng/umj203 https://www.mathnet.ru/eng/umj/v9/i2/p46
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Abstract page: | 41 | Full-text PDF : | 15 | References: | 15 |
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