We consider the notions of equicontinuity point, sensitivity point and so on from a topological point of view. Many of these notions can be sensibly defined either in terms of (finite) open covers or uniformities. We show that for the notions of equicontinuity point and sensitivity point, Hausdorff or uniform versions coincide in compact Hausdorff spaces and are equivalent to the standard definitions stated in terms of a metric in compact metric spaces. We prove that a uniformly chain transitive map with uniform shadowing property on a compact Hausdorff uniform space is either uniformly equicontinuous or it has no uniform equicontinuity points.

中文翻译：

---

一般拓扑空间中的等连续性、阴影和远侧性

我们从拓扑的角度考虑等连续点、敏感点等概念。许多这些概念可以根据（有限的）开放覆盖或均匀性来合理地定义。我们表明，对于等连续点和敏感点的概念，豪斯多夫或统一版本在紧致豪斯多夫空间中重合，并且等价于紧致度量空间中的度量标准定义。我们证明了在紧致 Hausdorff 均匀空间上具有均匀阴影属性的均匀链传递映射要么是均匀等连续的，要么没有均匀等连续点。