A note on convergence of double sequences in a topological space

Authors

  • Amar Kumar Banerjee Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India Author
  • Rahul Mondal Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India Author

Keywords:

double sequence, $d$-limit space, ${I}$-convergence, ${I}$-limit point, ${I}$-cluster point, ${I}$-sequential compactness

Subjects:

54A20, 40A35, 40A05

Abstract

In this paper we have shown that a double sequencein a topological space satisfies certain conditions which in turnare capable to generate a topology on a nonempty set. Also wehave used the idea of $I$-convergence of double sequences to studythe idea of $I$-sequential compactness in the sense of doublesequences [A.K. Banerjee, A. Banerjee, A note on $I$-convergenceand $I^{*}$-convergence of sequences and nets in a topologicalspace, Mat. Vesnik 67, 3 (2015), 212–221].

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Published

2017-04-15

Issue

Vol. 69 No. 2 (2017): Vol. 69, Issue 2

Section

Articles

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Copyright (c) 2017 Authors retain copyright to their work.

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This work is licensed under a Creative Commons Attribution 4.0 International License.