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

Ankur Sharmah, Debajit Hazarika

Published 2020-12-23Version 1

In this paper, we obtain some interesting results on $\mathcal{I}^\mathcal{K}$-convergence as well as on the relationships between different 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 also introduce a topological space namely $\mathcal{I}^\mathcal{K}$-sequential space and investigate some of its properties. $\mathcal{I}^\mathcal{K}$-notions of ideal cluster points and ideal limit points of a function are also introduced and characterized.