The extended persistence diagram is an invariant of piecewise linear functions, introduced by Cohen-Steiner, Edelsbrunner, and Harer. The bottleneck distance has been introduced by the same authors as an extended pseudometric on the set of extended persistence diagrams, which is stable under perturbations of the function. We address the question whether the bottleneck distance is the largest possible stable distance, providing an affirmative answer.

中文翻译：

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扩展持久性图的瓶颈距离的普遍性

扩展持久性图是分段线性函数的不变量，由 Cohen-Steiner、Edelsbrunner 和 Harer 引入。瓶颈距离是由同一作者引入的，作为扩展持久图集上的扩展伪度量，它在函数的扰动下是稳定的。我们解决了瓶颈距离是否是最大可能的稳定距离的问题，提供了肯定的答案。