对偶仿射不变点
Dual Affine invariant points
摘要：
R^n中凸体类上的一个仿射不变点，被赋予Hausdorff度量，是一个连续映射p，它在R^n上的一对一仿射变换A下不变，即p（A（K））=A（p（K））。本文通过对每个凸体K的公式q（K^{p（K）}）=p（K）定义仿射不变点p的对偶仿射点q的新概念，其中K^{p（K）}表示K关于p（K）的极。我们调查仿射不变点有一个对偶点，是否这个对偶点是唯一的，有自己的对偶点。我们定义了一个产品上的仿射不变点的集合，与对偶。最后，给出了一些例子，展示了仿射不变点集的丰富结构。
英文摘要：
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K^{p(K)})=p(K) for every convex body K, where K^{p(K)} denotes the polar of K with respect to p(K). We investigate which affine invariant points do have a dual point, whether this dual point is unique and has itself a dual point. We define a product on the set of affine invariant points, in relation with duality. Finally, examples are given which exhibit the rich structure of the set of affine invariant points.
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。
