This paper is devoted to the study of the medial axes of sets definable in polynomially bounded o-minimal structures, i.e. the sets of points with more than one closest point with respect to the Euclidean distance. Our point of view is that of singularity theory. While trying to make the paper self-contained, we gather here also a large bunch of basic results. Our main interest, however, goes to the characterization of those singular points of a definable, closed set \(X\subset {\mathbb {R}}^n\), which are reached by the medial axis.

中文翻译：

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中间轴和奇点。

本文致力于研究可在多项式有界o最小结构中定义的集合的中轴，即相对于欧几里得距离具有多个最近点的点的集合。我们的观点是奇点理论。在尝试使纸张独立时，我们在这里还收集了大量的基本结果。但是，我们的主要兴趣在于表征可定义的封闭集合\（X \ subset {\ mathbb {R}} ^ n \）的奇异点，这些奇点由中间轴到达。