MATEMATIČKI VESNIK Vol. 69, No. 2, pp. 144–152 (2017) 

A note on convergence of double sequences in a topological spaceAmar Kumar Banerjee and Rahul MondalDepartment of Mathematics, University of Burdwan, Golapbag, Burdwan713104, West Bengal, India. Email: akbanerjee@math.buruniv.ac.in, akbanerjee1971@gmail.com, imondalrahul@gmail.comAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
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