Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.

中文翻译：

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度量测度空间的拓扑方面

格罗莫夫在度量测度空间的同构类空间上引入了盒距离和可观测距离这两个距离函数，并发展了度量测度空间的收敛理论。我们研究了配备这些距离函数的空间的几种拓扑性质，以深入理解收敛理论。