A Note on $I$-Convergence and $I^{\star}$-Convergence of Sequences and Nets in Topological Spaces

Amar Kumar Banerjee, Apurba Banerjee

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.