$I?$ -Convergence of Double Sequences in Topological Groups

Abstract

Let $2N×N$ be a family of all subsets of N×N. Following the definition of ideal convergence in a metric space by Kostyrko et al. in2000, ideal convergence for double sequences in a metric space was introduced by Das et al. (2008). In this paper, I investigateI?-convergence and $I2$-convergence of double sequences in a topological space and establish some basic teorems. Furthermore weintroduce of $ I?$ -Cauchy and $I2$ -Cauchy notions for double sequences in topological groups.