Given two $n_i$-dimensional Alexandrov spaces $X_i$ of curvature $\ge 1$, the join of $X_1$ and $X_2$ is an $(n_1+n_2+1)$-dimensional Alexandrov space $X$ of curvature $\ge 1$, which contains $X_i$ as convex subsets such that their points are $\frac \pi2$ apart. If a group acts isometrically on a join that preserves $X_i$, then the orbit space is called quotient of join. We show that an $n$-dimensional Alexandrov space $X$ with curvature $\ge 1$ is isometric to a finite quotient of join, if $X$ contains two compact convex subsets $X_i$ without boundary such that $X_1$ and $X_2$ are at least $\frac \pi2$ apart and $\dim(X_1)+\dim(X_2)=n-1$.

中文翻译：

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亚历山德罗夫几何中连接的有限商

给定两个曲率$\ge 1$的$n_i$维Alexandrov空间$X_i$，$X_1$和$X_2$的连接是$(n_1+n_2+1)$维Alexandrov空间$X$的曲率$\ge 1$，其中包含 $X_i$ 作为凸子集，使得它们的点相距 $\frac \pi2$。如果一个群等距作用于一个保持 $X_i$ 的连接，那么轨道空间称为连接商。我们证明了具有曲率 $\ge 1$ 的 $n$ 维 Alexandrov 空间 $X$ 与有限的连接商等距，如果 $X$ 包含两个没有边界的紧凸子集 $X_i$ 使得 $X_1$ 和$X_2$ 至少相隔 $\frac \pi2$ 且 $\dim(X_1)+\dim(X_2)=n-1$。