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 functions. We address the question whether the bottleneck distance is the largest possible stable distance, providing an affirmative answer. Finally, we contrast the bottleneck distance with the interleaving distance of sheaves by showing that the interleaving distance of sheaves is not intrinsic, let alone universal.

翻译：延长的持久性图是科恩- 史蒂纳、爱德尔斯布龙纳和哈雷尔引入的片形线性函数的变数。 同一作者将瓶颈距离作为延展持久性图集的长假数来引入, 该图在功能的扰动下保持稳定。 我们处理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。 最后, 我们对比了瓶颈距离与夹层间距之间的距离, 我们通过显示夹层的间距不是内在的, 更不用说普遍性了 。