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

The goal is to show that a nonempty subset C⊆R is closed iff there is a continuous function g:R→R such that C=g−1(0).
1) Show the IF part. (Hint: explain why the inverse image of a closed set is closed.)
2) Show the ONLY IF part. (Hint: you may cite parts of Exercise 4.3.12 if needed.)

Expert Solution

Colby Messinger answered 2 years ago

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