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The goal is to show that a nonempty subset C⊆R is closed iff there is a...

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Advance Math

The goal is to show that a nonempty subset C⊆R isclosed iff there is a continuous function g:R→R such thatC=g−1(0).
1) Show the IF part. (Hint: explain why the inverse image of aclosed set is closed.)
2) Show the ONLY IF part. (Hint: you may cite parts of Exercise4.3.12 if needed.)

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