部分半群和VIP系统的广义中心集定理
Generalized central sets theorem for partial semigroups and vip systems
AI总结：
本文针对任意充分部分半群和VIP系统，完成了Phulara型广义中心集定理的推广，该定理此前已在交换半群及零附近等场景得到扩展。
摘要：
中心集定理最初由H. Furstenberg在动力系统领域提出。随后Hindman和Bergelson利用自然数集$\mathbb{N}$的Stone-$\check{C}$ech紧化$\beta\mathbb{N}$对该定理进行了扩展。在[SY]中，研究人员对半群的中心集进行了代数刻画，并证明了动力系统刻画与代数刻画的等价性。D. De、N. Hindman和D. Strauss证明了半群中心集定理的更强版本。D. Phulara通过取中心集序列将该定理推广到交换半群。最近J. Podder和S. Pal建立了零附近的Phulara型广义中心集定理。本文针对任意充分部分半群和VIP系统完成了此项推广工作。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
