  In this paper we have introduced the notion of $\mathcal{I}_{(s)}$-density
point corresponding to the family of unbounded and $\mathcal{I}$-monotonic
increasing positive real sequences, where $\mathcal{I}$ is the ideal of subsets
of the set of natural numbers. We have studied the corresponding topology in
the space of reals and have investigated several properties of this topology.
Also we have formulated a weaker condition for the sequences so that the
classical density topology coincides with $\mathcal{I}_{(s)}$-density topology.
