On sparse set topology using ideals in the space of reals
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| Format: | Preprint |
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2024
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| _version_ | 1866914974571429888 |
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| author | Debnath, Indrajit Banerjee, Amar Kumar |
| author_facet | Debnath, Indrajit Banerjee, Amar Kumar |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sparse set topology using ideals in the space of reals Debnath, Indrajit Banerjee, Amar Kumar General Topology 26E99, 54C30, 40A35 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. |
| title | On sparse set topology using ideals in the space of reals |
| topic | General Topology 26E99, 54C30, 40A35 |
| url | https://arxiv.org/abs/2410.12503 |