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

In this paper, we obtain some results on the relationships between different ideal \linebreak convergence modes namely, ${\mathcal{I}}^{\mathcal{K}}$, ${\mathcal{I}}^{{\mathcal{K}}^{\ast }}$, $\mathcal{I}$, $\mathcal{K}$, $$\mathcal{I}$ \cup $\mathcal{K}$$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 $X$.