Prove part 3 of Theorem 3.2.2. (Hint: Use the trick in the proof of the second part of the theorem along with Exercise 1.)
Exercise 1
Prove that if f : U ⊂ ℝn → ℝ and a is such that for some number b, then there exists r > 0 such that f(x) ≠ b for all x in the set Br(a) ∩ U.
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