On the concept of generalization of I-density points

This paper deals with essential generalization of \(\mathcal{I}\)-density points and \(\mathcal{I}\)-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.