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arXiv · 2407.02629

Generalized central sets theorem for partial semigroups and vip systems

Anik Pramanick·MD Mursalim Saikh
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Abstract

The Central sets theorem was first introduced by H. Furstenberg [F] in terms of Dynamical systems. Later Hindman and Bergelson extended the theorem using Stone-$Č$ech compactification $β$$\mathbb{N}$ of $\mathbb{N}$. In [SY] algebraic characterization of Central sets was done for semigroup and equivalence of Dynamical and Algebraic characterizations were shown. D. De, N. Hindman, and D. Strauss proved a stronger version of the Central sets theorem for semigroup. D. Phulara generalized that theorem for commutative semigroup taking a sequence of Central sets. Recently J. Podder and S. Pal established the Phulara type generalization of Central sets theorem near zero [PP]. We did this for arbitrary adequate partial semigroup and VIP systems.

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Anik Pramanick, MD Mursalim Saikh. 2025-02-14. Generalized central sets theorem for partial semigroups and vip systems. https://arxiv.org/abs/2407.02629

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