I₂-CONVERGENCE AND I₂-CAUCHY DOUBLE SEQUENCES IN TOPOLOGICAL GROUPS

Ömer Kişi

Abstract


Let  be a family of all subsets of N×N. Following the definition of ideal convergence in a metric space by Kostyrko et al. in 2000, ideal convergence for double sequences in a metric space was introduced by Das et al. (2008). In this paper, I inverstigate I-convergence and -convergence of double sequences in a topological space and establish some basic teorems. Furthermore we introduce of I-Cauchy and -Cauchy notions for double sequences in topological groups.


Keywords


I₂-convergence, I_2^*-convergence, topological group, double sequence, ideal.

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DOI: http://dx.doi.org/10.7212%2Fzkufbd.v8i1.804

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