| A note on $I$-convergence and $I^{\star}$-convergence of sequences and nets in topological spaces |
| Amar Kumar Banerjee and Apurba Banerjee |
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 important topological properties. Further we derive characterization of compactness in terms of these concepts. We introduce also the idea of $I$-sequentially compactness and derive a few basic properties in a topological space.
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Keywords: ${I}$-convergence; ${I}^{\star}$-convergence; ${I}$-limit point; ${I}$-cluster point; ${I}$-sequentially compact. |
MSC: 54A20, 40A35 |
Pages: 212--221 |
Volume 67 , Issue 3 , 2015 |
