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Show that the set $\{ x \in [ a,b ] : f(x) = g(x)\}$ is closed in $\Bbb R$.

I was wondering if some one can answer my following question:

Suppose $f$ and $g$ are continuous real valued functions. Then show the set $A=\{x|f(x)=g(x)\}$ is closed.

Thanks

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    Observe that if this $(f-g)^{-1}(\{0\})$2012-09-17
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    What is the definition of closed set that you are working with?2012-09-17
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    See here: [Show that the set $\{ x \in \[ a,b \] : f(x) = g(x)\}$ is closed in $\Bbb R$.](http://math.stackexchange.com/questions/144480/show-that-the-set-x-in-a-b-fx-gx-is-closed-in-bbb-r)2012-09-17

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