Abstract In Topological Data Analysis, persistence diagrams are a useful tool for visualizing persistent homology. It is proved that the set of persistence diagrams endowed with the bottleneck distance is homeomorphic to the pre-Hilbert space of finitary sequences. We also consider a bitopological space of persistence diagrams and describe its topology.

中文翻译：

---

在一组持久性图上描述拓扑

摘要 在拓扑数据分析中，持久图是可视化持久同源性的有用工具。证明了赋予瓶颈距离的持久图集同构于有限序列的前希尔伯特空间。我们还考虑了持久图的双拓扑空间并描述了它的拓扑。