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Ural Mathematical Journal, 2023, Volume 9, Issue 2, Pages 46–59
DOI: https://doi.org/10.15826/umj.2023.2.004
(Mi umj203)
 

$\mathcal{I}^{\mathcal{K}}$-sequential topology

H. S. Behmanush, M. Küçükaslan

Mersin Üniversitesi
References:
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.
Bibliographic databases:
Document Type: Article
Language: English
Citation: H. S. Behmanush, M. Küçükaslan, “$\mathcal{I}^{\mathcal{K}}$-sequential topology”, Ural Math. J., 9:2 (2023), 46–59
Citation in format AMSBIB
\Bibitem{BehKuc23}
\by H.~S.~Behmanush, M.~K\"u{\c c}\"ukaslan
\paper $\mathcal{I}^{\mathcal{K}}$-sequential topology
\jour Ural Math. J.
\yr 2023
\vol 9
\issue 2
\pages 46--59
\mathnet{http://mi.mathnet.ru/umj203}
\crossref{https://doi.org/10.15826/umj.2023.2.004}
\elib{https://elibrary.ru/item.asp?id=59690645}
\edn{https://elibrary.ru/CMMYPK}
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