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MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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].

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

MSC: 54A20, 40A35, 40A05

Pages:  144--152     

Volume  69 ,  Issue  2 ,  2017