Math 318 HW #4
Due 5:00 PM Thursday, February 24
Reading:
Abbott §7.7, Wilcox & Myers Chapter 2.
Problems:
1. Abbott Exercise 7.4.6.
2. Abbott Exercise 7.4.7
3. Abbott Exercise 7.6.11.
4. Abbott Exercise 7.6.13. You should assume the result of Exercise
SN 7.6.12, which is straightforward: since there are finitely many Gn , the set K = [a, b]\ n=1 Gn is a finite union of
closed, bounded intervals and, therefore, compact. The proof that an α-continuous function
on a compact set is uniformly α-continuous is similar to the proof that a continuous function
on a compact set is uniformly continuous (see also Exercise 7.6.9).
5. Wilcox & Myers Exercise 9.3 (p. 26).
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