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## Homework Statement

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

## Homework Equations

## 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.