On Kuratowski I-Convergence of Sequences of Closed Sets

Talo, Ö; Sever, Y

On Kuratowski I-Convergence of Sequences of Closed Sets

Authors

Talo, Ö

Sever, Y

Publisher

UNIV NIS, FAC SCI MATH

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 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.