On a generalized density point defined by families of sequences involving ideals

We introduce 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 study the corresponding topology in the space of reals and investigate several properties of this topology. Also we present a characterization of equality between the classical density topology and $\mathcal{I}_{(s)}$-density topology.