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。
We characterize almost periodicity with equicontinuity, and prove that if the group is uniform equicontinuous then it is topologically equivalent to an isometric one.
连续、一致连续、一致收敛和等度连续是函数或函数列非常重要的性质。
Continuity, uniform continuity, uniform convergence and equicontinuity are very important qualities of functions or sequence of functions.
定理3 X是囿空间的充要条件为：每个从X到Y的一致有界的线性算子族都是等度连续的。
Theorem 3 X is a bornologic space if and only if every uniformly bounded set of linear operators from X to Y is equicontinuous.
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