Proof of the Extreme Value Thm

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This video proves the fact that a continuous map from a compact set to the real line achieves a maximum and minimum value.
  1. Linda Green
  2. topology
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Автор

Thank you for the proof. I have a question though. Can we use the fact that f(X) is closed and bounded to say that f(X) contains lower and upper bounds? I believe, in your proof, you have used the fact that f(X) is bounded anyway as when you are using (-inf, f(a)) open intervals, we are assuming that f(a) is not minus infinity right?

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Автор

I don't understand the thumbs down. The only rigorous proof I found on here.

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