Hindman and Leader introduced the set \(0^{+}\) of ultrafilters on \(\left( 0,1\right) \), characterized the smallest ideal of \(\left( 0^{+},+\right) \) and proved the Central Set Theorem near 0. Recently Polynomial Central Set Theorem has been proved by Bergelson, Johnson Jr. and Moreira. In this note, we will Polynomial Central Set Theorem near 0.

中文翻译：

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多项式中心集定理接近零

Hindman和Leader引入了\（\ left（0,1 \ right）\）上的超滤子集\（0 ^ {+} \），其特征是\（\ left（0 ^ {+}，+ \右）\），并证明了中心集定理在0附近。最近，多项式中心集定理已由Bergelson，Johnson Jr.和Moreira证明。在本说明中，我们将多项式中央集定理设为0附近。