Preservation of notion of large sets near zero over reals

2025/12/02 by Kilangbenla Imsong, Imsong, Kilangbenla, Ram Paul +1
Mathematics · #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2512.02596

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 ∈ ℕ, M is a u × v matrix satisfying restrictions that vary with the notion of largeness and if Ψ is a notion of large sets in ℕ then \x ∈ ℕ^v: Mx ∈ Ψ^u\ is large set in ℕ^v. In this article, we investigate the above result for various notions of largeness near zero in ℝ⁺.

Citations

• Preservation of notion of C sets near zero over reals

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