论文标题
公制转换空间的收敛性
Convergence of metric transformed spaces
论文作者
论文摘要
我们考虑度量度量空间/金字塔的度量转换。我们阐明了从原始序列的转化空间序列获得的融合的条件，相反，分别从转化序列的序列获得了原始序列的收敛性。作为一种应用，我们证明了具有标准riemannian距离的球形和投影空间分别收敛到高斯空间和高斯空间的HOPF商，因为尺寸差异为无穷大。
We consider the metric transformation of metric measure spaces/pyramids. We clarify the conditions to obtain the convergence of the sequence of transformed spaces from that of the original sequence, and, conversely, to obtain the convergence of the original sequence from that of the transformed sequence, respectively. As an application, we prove that spheres and projective spaces with standard Riemannian distance converge to a Gaussian space and the Hopf quotient of a Gaussian space, respectively, as the dimension diverges to infinity.
