A common criterion for uniform convergence and introduction to bounded continuous function

A common criterion for uniform convergence and introduction to a bounded continuous function

0:00 start
0:30 we prove that on a compact set, the monotone continuous function converges uniformly if we assume its convergent function is continuous.
7:13 introduction to a bounded continuous function
8:00 show bounded continuous function is a complete metric space

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We proved that under uniform convergence, one can prove that the limit and the differential can be exchanged.

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