A note on convergence of double sequences in a topological space

Amar Kumar Banerjee and Rahul Mondal

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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