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

Abstract

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.