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A common criterion for uniform convergence and introduction to bounded continuous function
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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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Advanced mathematics list:
Group representation for finite group
exact sequences
Ring theory lecture
group theory lecture
Category theory
Field theory in abstract algebra
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Please subscribe to my channel if you like it
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
Please subscribe to my channel
We proved that under uniform convergence, one can prove that the limit and the differential can be exchanged.
Subscribe to my channel
Advanced mathematics list:
Group representation for finite group
exact sequences
Ring theory lecture
group theory lecture
Category theory
Field theory in abstract algebra
Mathematical analysis
Please subscribe to my channel if you like it
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