Sequential Characterization of Uniform Continuity

We define what it means for two sequences to be equiconvergent and then give a sequential characterization of uniform continuity. We finish with an example of a showing that function that is not uniformly continuous.

0:00, Intro
0:35, Review of Sequential Characterization of Continuity
1:30, Definition of Equiconvergent
4:21, Thm of Sequential Characterization of Uniform Continuity
6:14, Proof: Thm of Sequential Characterization of Uniform Continuity (forward direction)
10:36, Proof: Thm of Sequential Characterization of Uniform Continuity (backward direction)
14:45, Porism: Sequential Failure of Uniform Continuity (a consequence of the proof)
17:35, Example that uses the Porism