We characterize almost periodicity with equicontinuity, and prove that if the group is uniform equicontinuous then it is topologically equivalent to an isometric one.

本文对一致空间上的群作用，用等度连续性刻画了几乎周期的性质，并且论证了一致等度连续的群作用拓扑等价于一等距的群作用。

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It says that if in this space any closed-curve object, such as a rubber band, can be shrunk to a point, then the space is topologically equivalent to a sphere.

FORBES: Plugging A Math Gap