论文标题
$ \ Mathcal {i}^{\ Mathcal {k}} $ - 拓扑空间中收敛的其他方面
Further aspects of $\mathcal{I}^{\mathcal{K}}$-convergence in Topological Spaces
论文作者
论文摘要
在本文中，我们获得了一些有关不同理想\界限收敛模式之间关系的结果\ Cup \ Mathcal {K} $和$（\ Mathcal {I} \ Cup \ Mathcal {K}）^*$。我们引入了拓扑空间，即$ \ MATHCAL {i}^\ MATHCAL {K} $ - 顺序空间，并显示$ \ Mathcal {I}^\ Mathcal {k} $ - sequential-sequential-sequential Spaces包含顺序空间。此外，此处还介绍了$ \ MATHCAL {I}^\ MATHCAL {K} $ - 集群点的概念和函数的限制点。对于拓扑空间中的给定序列$ x $，我们表征了$ \ MATHCAL {i}^\ MATHCAL {k} $ - 序列的群集点作为$ x $的封闭子集。
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 $X$.
