In this expository paper, we discuss several types of independence of points in the Euclidean space ${\mathbb{R}}^d$ such as algebraic independence, strong independence, weak independence, and give a detailed geometric proof of their interrelationship. We also give yet another proof of Reay’s theorem determining the dimension of a Tverberg set.

中文翻译：

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强大的独立性和特维尔贝格的规模

在此说明性论文中，我们讨论了欧几里得空间中点的几种独立性 ${\mathbb{[R}}^d$例如代数独立性，强独立性，弱独立性，并给出它们之间相互关系的详细几何证明。我们还给出了Reay定理的另一个证明，该定理确定了Tverberg集的维数。