Polynomial central set theorem near zero

TL;DR

This paper extends the Polynomial Central Set Theorem to the context near zero, building on prior work on ultrafilters and central sets in additive semigroups, providing new insights into algebraic structures in analysis.

Contribution

It proves the Polynomial Central Set Theorem near zero, a significant generalization of existing theorems in the area of ultrafilters and algebraic combinatorics.

Findings

Established the Polynomial Central Set Theorem near zero.

Extended the characterization of ultrafilters to the near zero setting.

Contributed to the understanding of algebraic structures in analysis.

Abstract

N. Hindman and I. Leader introduced the set of ultrafilters 0+ on (0,1) and characterize smallest ideal of (0+,+) and proved the Central Set Theorem near zero. Recently Polynomial Central Set Theorem has been proved by V. Bergelson, J. H. Johnson Jr. and J. Moreira. In this article, we will prove Polynomial Central Set Theorem near zero.