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arXiv · 2512.02596

Preservation of notion of large sets near zero over reals

Kilangbenla Imsong·Ram Krishna Paul
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Abstract

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 $\Psi$ is a notion of large sets in $\mathbb{N}$ then $\{\vec{x} \in \mathbb{N}^v: M\vec{x} \in \Psi^u\}$ is large set in $\mathbb{N}^v$. In this article, we investigate the above result for various notions of largeness near zero in $\mathbb{R}^+$.

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Kilangbenla Imsong, Ram Krishna Paul. 2025-12-02. Preservation of notion of large sets near zero over reals. https://arxiv.org/abs/2512.02596

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