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Homework 10, Advanced Calculus 1

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Homework 10, Advanced Calculus 1

1. Rudin Chapter 7 Exercise 18 2. Rudin Chapter 7 Exercise 19 3. Rudin Chapter 7 Exercise 20 4. Rudin Chapter 7 Exercise 22

5. Prove that the conditions ”A separates points” and ”A vanishes at no point” are both indispensable for the generalized Stone-Weierstrass Theorem (Thm. 7.31). That is, the theorem is false if either condition is missing.

6. Rudin Chapter 7 Exercise 24, the first two proofs ”|fp(x)| ≤ d(a, p) ... and ”kfp− fqk = d(p, q) ...” .

7. Rudin Chapter 7 Exercise 24, the last statement ”Y is complete.”

8. Rudin Chapter 7 Exercise 14 9. Rudin Chapter 7 Exercise 21 10. Rudin Chapter 7 Exercise 23

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