HW - due Oct. 29 (deadline extended!)

part of 2.51: Denote oscf(x)=h(x)-g(x) (also denoted omegaf(x); see notes in class on Thursday, Oct. 17).
Show that

  1. oscf(x)=0  <=>  f is continuous at  x
  2. show that the set {x | oscf(x) < a} is open for each real number a.
    NOTE (10/22): the inequality is "< ", not "> " as I first wrote.
(We will use this to prove Proposition 4.7.)

2.53: I mentioned a hint long time ago (when we discussed Chapter 2?) in class. Use the results of 2.51 above.