On density topology using ideals in the space of reals

TL;DR

This paper introduces the concept of ensity topology in real spaces using ideals of natural numbers, exploring its properties and separation axioms to deepen understanding of topological structures influenced by ideals.

Contribution

It defines ensity topology based on ideals, introduces upper and lower ensity, and studies their separation axioms, advancing the theoretical framework of density topologies.

Findings

Defined ensity topology in als of reals

Analyzed separation axioms of the ensity topology

Explored properties of upper and lower ensity

Abstract

In this paper we have introduced the notion of $\mathcal{I}$-density topology in the space of reals introducing the notions of upper $\mathcal{I}$-density and lower $\mathcal{I}$-density where $\mathcal{I}$ is an ideal of subsets of the set of natural numbers. We have further studied certain separation axioms of this topology.