On some topology generated by $\mathcal{I}$-density function

Indrajit Debnath; Amar Kumar Banerjee

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arXiv · 2307.10777

On some topology generated by $\mathcal{I}$-density function

Indrajit Debnath·Amar Kumar Banerjee

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Abstract

In this paper we have studied on $\mathcal{I}$-density function using the notion of $\mathcal{I}$-density, introduced by Banerjee and Debnath \cite{banerjee 4} where $\mathcal{I}$ is an ideal of subsets of the set of natural numbers. We have explored certain properties of $\mathcal{I}$-density function and induced a topology using this function in the space of reals namely $\mathcal{I}$-density topology and we have given a characterization of the Lebesgue measurable subsets of reals in terms of Borel sets in $\mathcal{I}$-density topology.

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BibTeX RIS

Indrajit Debnath, Amar Kumar Banerjee. 2023-07-20. On some topology generated by $\mathcal{I}$-density function. https://arxiv.org/abs/2307.10777

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