Theorems about Continuous Functions Part 3 - Uniform Continuity
Update: 2022-11-15
Description
In this episode we introduce a new concept regarding continuity, namely uniform continuity. For continuity, for given deviation of function values, the allowed deviation of corresponding pre-images depends on the point, where continuity is analysed. In contrast, for uniform continuity, the allowed deviation of pre-images can be chosen independently of the point considered and only depends on the initially allowed deviation of function values. There are examples that show that uniform continuity is strictly stronger than continuity. However, if a function is defined on a sequentially compact metric space, continuity is already enough to yield uniform continuity.
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