论文标题
关于古典凸理论的新颖观点
Novel view on classical convexity theory
论文作者
论文摘要
令$ b_ {x} \ subseteq \ mathbb {r}^{n} $表示用直径$ [0，x] $的欧几里得球，即带有$ \ frac {x} {x} {2} {2} {2} $的中心，and radius $ \ frac $ \ frac $ \ frac {\ frac {\ weft | x \ x \ x \ right | x \ right | right | right | right | right | right |我们称这样的球为花瓣。花$ f $是任何花瓣的结合，即$ f = \ bigcup_ {x \ in}} b_ {x} $的任何集合$ a \ subseteq \ subseteq \ mathbb {r}^{n} $。我们在以前的工作中表明，所有花的家族$ \ nathcal {f} $与$ \ Mathcal {k} _ {0} $在1-1通信中 - 所有凸体的家族中，所有凸起的物体都包含$ 0 $。实际上，有两个本质上不同的对应关系。我们在$ \ Mathcal {f} $和$ \ Mathcal {k} _ {0} $上演示了许多不同的非线性构造。为了实现这一目标，我们进一步发展了鲜花理论。
Let $B_{x}\subseteq\mathbb{R}^{n}$ denote the Euclidean ball with diameter $[0,x]$, i.e. with with center at $\frac{x}{2}$ and radius $\frac{\left|x\right|}{2}$. We call such a ball a petal. A flower $F$ is any union of petals, i.e. $F=\bigcup_{x\in A}B_{x}$ for any set $A\subseteq\mathbb{R}^{n}$. We showed in previous work that the family of all flowers $\mathcal{F}$ is in 1-1 correspondence with $\mathcal{K}_{0}$ - the family of all convex bodies containing $0$. Actually, there are two essentially different such correspondences. We demonstrate a number of different non-linear constructions on $\mathcal{F}$ and $\mathcal{K}_{0}$. Towards this goal we further develop the theory of flowers.
