持久图集合上的强拓扑
Strong topology on the set of persistence diagrams
摘要：
我们赋予持久图集强拓扑（瓶颈距离内有界子集的递增序列的可数直极限的拓扑）。所得到的空间的拓扑结构进行了描述。证明了具有瓶颈度量的持久图空间在Gromov意义下具有无穷渐近维数。
英文摘要：
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.
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