Suppose that E is a compact subset of X. a) If f, g : E Rn
Question:
a) If f, g : E → Rn are uniformly continuous, prove that f + g and f ∙ g are uniformly continuous. Did you need compactness for both results?
b) If g: E → R is continuous on E and g(x) ≠ 0 for x ∈ £, prove that 1/g is a bounded function.
c) If f, g: E → R are uniformly continuous on E and g(x) ≠ 0 for x ∈ E, prove that f/g is uniformly continuous on £.
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Step by Step Answer:
a Repeat the proof of Exercise 345ab Compactness was used to prove fg is uniformly continuous ...View the full answer
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