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arXiv 2012.124842020-12math.GN

Further aspects of $\mathcal{I}^{\mathcal{K}}$-convergence in Topological Spaces

Ankur Sharmah, Debajit Hazarika

备注：: 10 page

英文摘要：

In this paper, we obtain some results on the relationships between different ideal \linebreak convergence modes namely, $\mathcal{I}^\mathcal{K}$, $\mathcal{I}^{\mathcal{K}^*}$, $\mathcal{I}$, $\mathcal{K}$, $\mathcal{I} \cup \mathcal{K}$ and $(\mathcal{I} \cup \mathcal{K})^*$. We introduce a topological space namely $\mathcal{I}^\mathcal{K}$-sequential space and show that the class of $\mathcal{I}^\mathcal{K}$-sequential spaces contain the sequential spaces. Further $\mathcal{I}^\mathcal{K}$-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space $X$, we characterize the set of $\mathcal{I}^\mathcal{K}$-cluster points of the sequence as closed subsets of $X$.

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