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

Abstract

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 $(\mathcal{I}\cup \mathcal{K}{)}^{\ast }$. 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 $X$.

10 page

Cited by in corpus (1)

• On $I^K$-Convergence in a Topological space via semi-open sets