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1·Theorem 3 X is a bornologic space if and only if every uniformly bounded set of linear operators from X to Y is equicontinuous.

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。

2·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。

3·In this paper, the following two properties of compact system be proved; (1) a factor of a minimal system is minimal; (2) a factor of an equicontinuous system is equicontinuous system.

证明了紧致系统的2个性质：1极小系统的因子是极小的；2等度连续系统的因子是等度连续的。

4·By discussing the filter product cosine operator function and the spectrum of it 's generator, the spectral mapping theorem for the locally equicontinuous cosine operator function is established.

通过对滤子积余弦算子函数及生成元谱性质的讨论，建立了局部等度连续余弦算子函数的谱映象定理。