论文标题
一组持久图的强大拓扑
Strong topology on the set of persistence diagrams
论文作者
论文摘要
我们将持久图的集合赋予了强大的拓扑结构（在瓶颈距离中考虑的有界子集的序列增加的直接限制的拓扑）。描述了所获得的空间的拓扑。 另外，我们证明，瓶颈度量标准的持久图在Gromov意义上具有无限的渐近维度。
We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described. Also, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.
