Let f be defined and continuous on a closed set S in R. Let A={x: x S and f(x)=0}. Prove that A is a closed subset of R .
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Originally Posted by janae77 Let f be defined and continuous on a closed set S in R. Let A={x: x S and f(x)=0}. Prove that A is a closed subset of R . Hint: If is continues and then there is an open interval such that and is non-zero on . Hence, does this show the complement open?
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