IDEAL CONVERGENCE OF DOUBLE SEQUENCES OF CLOSED SETS

Abstract

In the present paper, we introduce the concepts of ideal inner and ideal outer limits which always exist even if empty sets for double sequences of closed sets in Pringsheim's sense. Next, we give some formulas for finding ideal inner and outer limits in a metric space. After then, we define Kuratowski ideal convergence of double sequences of closed sets by means of the ideal inner and ideal outer limits of a double sequence of closed sets. Additionally, we give some examples that our result is more general than the results obtained before.