论文标题
许多三角形是退化的度量空间
Metric spaces in which many triangles are degenerate
论文作者
论文摘要
里士满和里士满（Amer。Math。Math。104（1997），713--719）证明了以下定理：如果在至少五个点的度量空间中，所有三角形都是退化的，那么该空间是对真实行的子集等等距。我们证明该假设不必要地很强：实际上，$θ（n^2）$适当地放置了退化的三角形。
Richmond and Richmond (Amer. Math. Monthly 104 (1997), 713--719) proved the following theorem: If, in a metric space with at least five points, all triangles are degenerate, then the space is isometric to a subset of the real line. We prove that the hypothesis is unnecessarily strong: In fact, $Θ(n^2)$ suitably placed degenerate triangles suffice.
