The path connectedness of spheres in Gromov-Hausdorff space is studied. It is proved that (1) each sphere centered at the single point space is path connected; (2) for any compact metric space X there exists a number R_X such that each sphere centered at X and whose radius is greater than R_X is path connected.

中文翻译：

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Gromov-Hausdorff空间中球的路径连通性

研究了Gromov-Hausdorff空间中球的路径连通性。证明（1）以单点空间为中心的每个球都是路径连接的；（2）对于任何紧凑的度量空间X，都存在一个数R _X，使得以X为中心且半径大于R _X的每个球都是路径连接的。