Vol. 69, No. 2, pp. 144–152 (2017)

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A note on convergence of double sequences in a topological space

Amar Kumar Banerjee and Rahul Mondal

Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India. E-mail: akbanerjee@math.buruniv.ac.in, akbanerjee1971@gmail.com, imondalrahul@gmail.com

Abstract: In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a nonempty set. Also we have used the idea of I-convergence of double sequences to study the idea of I-sequential compactness in the sense of double sequences [A.K. Banerjee, A. Banerjee, A note on I-convergence and I * -convergence of sequences and nets in a topological space, Mat. Vesnik 67, 3 (2015), 212–221].

Keywords: double sequence; d-limit space; I-convergence; I-limit point; I-cluster point; I-sequential compactness.

Classification (MSC2000): 54A20; 40A35, 40A05

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Electronic fulltext finalized on: 24 Feb 2017. This page was last modified: 17 Mar 2017.

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