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 Başar) 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 positive 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.