On Kuratowski i-convergence of sequences of closed sets

Abstract

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