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Math Help - Continuity

  1. #1
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    Continuity

    Let f be defined and continuous on a closed set S in R. Let A={x: x \inS and f(x)=0}.
    Prove that A is a closed subset of R .
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  2. #2
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    Quote Originally Posted by janae77 View Post
    Let f be defined and continuous on a closed set S in R. Let A={x: x \inS and f(x)=0}.
    Prove that A is a closed subset of R .
    Hint: If f is continues and f(p)\not=0 then there is an open interval such that p\in (s,t) and f is non-zero on (s,t).
    Hence, does this show the complement open?
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