On sparse set topology using ideals in the space of reals

Indrajit Debnath; Amar Kumar Banerjee

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arXiv · 2410.12503

On sparse set topology using ideals in the space of reals

Indrajit Debnath·Amar Kumar Banerjee

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Abstract

In this paper we have introduced the notion of $\mathcal{I}$-sparse set in the space of reals and explored some properties of the family of $\mathcal{I}$-sparse sets. Thereafter we have induced a topology namely $\mathcal{I}$-sparse set topology in the space of reals and it has been observed that this topology is finer than $\mathcal{I}-$density topology introduced by Banerjee and Debnath in \cite{banerjee 4}. We further studied some salient properties of this topology.

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BibTeX RIS

Indrajit Debnath, Amar Kumar Banerjee. 2024-10-16. On sparse set topology using ideals in the space of reals. https://arxiv.org/abs/2410.12503

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