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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.02596 |
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| _version_ | 1866912743029735424 |
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| author | Imsong, Kilangbenla Paul, Ram Krishna |
| author_facet | Imsong, Kilangbenla Paul, Ram Krishna |
| contents | The study of the size of subsets in a semigroup have shown that many of these subsets have strong combinatorial properties and contribute richly to the algebraic structure of the Stone-Cech compactification of a discrete semigroup. N. Hindman and D. Strauss have proved that if u, v $\in \mathbb{N}$, M is a u \times v matrix satisfying restrictions that vary with the notion of largeness and if $Ψ$ is a notion of large sets in $\mathbb{N}$ then $\{\vec{x} \in \mathbb{N}^v: M\vec{x} \in Ψ^u\}$ is large set in $\mathbb{N}^v$. In this article, we investigate the above result for various notions of largeness near zero in $\mathbb{R}^+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Preservation of notion of large sets near zero over reals Imsong, Kilangbenla Paul, Ram Krishna Combinatorics The study of the size of subsets in a semigroup have shown that many of these subsets have strong combinatorial properties and contribute richly to the algebraic structure of the Stone-Cech compactification of a discrete semigroup. N. Hindman and D. Strauss have proved that if u, v $\in \mathbb{N}$, M is a u \times v matrix satisfying restrictions that vary with the notion of largeness and if $Ψ$ is a notion of large sets in $\mathbb{N}$ then $\{\vec{x} \in \mathbb{N}^v: M\vec{x} \in Ψ^u\}$ is large set in $\mathbb{N}^v$. In this article, we investigate the above result for various notions of largeness near zero in $\mathbb{R}^+$. |
| title | Preservation of notion of large sets near zero over reals |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.02596 |