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  3. let f : r ? r be a function. (a) prove that f is c

Let f : R ? R be a function. (a) Prove that f is continuous on...

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Advance Math

Let f : R ? R be a function.

(a) Prove that f is continuous on R if and only if, for everyopen set U ? R, the preimage f ?1 (U) = {x ? R : f(x) ? U} isopen.

(b) Use part (a) to prove that if f is continuous on R, its zeroset Z(f) = {x ? R : f(x) = 0} is closed.

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