On the concept of generalization of I-density points

Abstract

This paper deals with essential generalization of $\mathcal{I}$-density points and I-density topology. In particular, there is an example showing that this generalization of $\mathcal{I}$-density point yields the stronger concept of density point than the notion of $\mathcal{I}(\mathcal{J})$-density. Some properties of topologies generated by operators related to this essential generalization of density points are provided.