On Kuratowski $\mathcal I$-Convergence of Sequences of Closed Sets

Özer Talo, Yurdal Sever

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Başar) to $\mathcal I$-inner and $\mathcal I$-outer limits and give some $\mathcal I$-analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where $\mathcal I$ is an ideal of subsets of the set $\mathbb N$ of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski $\mathcal I$-convergence for a sequence of closed sets and get some properties for Kuratowski $\mathcal I$-convergent sequences. Also, we examine the relationship between Kuratowski $\mathcal I$-convergence and Hausdorff $\mathcal I$-convergence.