(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

assume h: R->R is continuous on R and let K={x: h(x)=0}. Show that K is a closed set.

2. Relevant equations

3. The attempt at a solution

since we know h is continuous and h(x)=0. therefore, we know there is a epsilon neighborhood such that x belongs to preimage f^(-1)({0}). I got stuck up to this step since h maps all x's in R to 0 so this could mean all members in R so i don't see it's a closed set at all. please help. i'm confused with this concept.

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# Homework Help: Proof on continuous functions

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