A note on $I$-convergence and $I^{\star}$-convergence of sequences and nets in topological spaces

Authors

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

Keywords:

${I}$-convergence, ${I}^{\star}$-convergence, ${I}$-limit point, ${I}$-cluster point, ${I}$-sequentially compact

Subjects:

54A20, 40A35

Abstract

In this paper, we use the idea of $I$-convergence and$I^{\star}$-convergence of sequences and nets in a topological space to study some importanttopological properties. Further we derive characterization of compactness in terms of theseconcepts. We introduce also the idea of $I$-sequentially compactness and derive a few basicproperties in a topological space.

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Published

2015-07-15

Issue

Vol. 67 No. 3 (2015): Vol. 67, Issue 3

Section

Articles

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Copyright (c) 2015 Authors retain copyright to their work.

Creative Commons License

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