Functional Analysis 16 | Compact Sets

Published: 07 November 2020
on channel: The Bright Side of Mathematics
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🌙 There is also a dark mode version of this video:    • Functional Analysis 16 | Compact Sets...  
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This is my video series about Functional Analysis where we start with metric spaces, talk about operators and spectral theory, and end with the famous Spectral Theorem. I hope that it will help everyone who wants to learn about it.

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00:00 Introduction
00:40 Compactness in R^n
01:46 Definition: sequentially compact
04:00 Examples
05:52 Proposition: compact implies closed and bounded
07:14 Proof

#FunctionalAnalysis
#VectorSpaces
#Mathematics
#LearnMath
#calculus

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)


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