Continuity and Compactness

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What happens when you apply a continuous function to a compact set, and why does it matter? Watch this video to find out!

  1. Dr Peyam
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Комментарии
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The proof from 9:40 onward was great! it's quite abstract but drawing all the blobs covering K and f(K) really helped.

FT
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Dude I love your content. Your enthusiasm for mathematics is a gift to humanity.

davidsanjenis
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The proof I was shown in school used the boundedness theorem to prove the extreme value theorem, except we had never proved the boundedness theorem! I appreciate you starting basically from scratch.

youtubeviolatedme
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Interesting concepts put together! Awesome work!

RCSmiths
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I can't believe this videos shows up right in time! We are doing that kind of stuff in Uni right now and your explanations are fantastic :) Greetings from Germany!

End_V
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I always wondered something: should we have additional assumptions on f()? At least that it is well behaved? because 1/x is certainly continuous but it is not bounded in [0 1] even though [0 1] is compact.

albertornstein
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Is there a theorem which guarantees that an open cover exists for any topological space?

mathgeek