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Homework 6, Advanced Calculus 1

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Homework 6, Advanced Calculus 1

!!! Please note the new group and classroom assignment !!!

1. Rudin Chapter 3 Exercise 24ab.

2. Rudin Chapter 3 Exercise 24c.

3. Rudin Chapter 3 Exercise 24d.

4. Rudin Chapter 3 Exercise 24e.

5. Rudin Chapter 3 Exercise 21.

6. Rudin Chapter 3 Exercise 22.

7. Rudin Chapter 3 Exercise 23.

8. Given f : A → B and {Eα} a collection of subsets of B, prove that (a) f−1(∪αEα) = ∪αf−1(Eα).

(b) f−1(∩αEα) = ∩αf−1(Eα).

(c) f−1(Eαc) = f−1(Eα)c.

9. Prove that 8a is still true with f−1 replaced by f , but 8b and 8c no longer hold.

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