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Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is:

ConsiderC[0,1] with the sup metric. Let f:[0,1]→Rbe the function given by f(x)=x²+2

Let A={g ЄC[0,1]: d(g,f) > 3}. Prove that A is an open set

Let B={g ЄC[0,1]: 1 ≤ d(g,f) ≤ 3}. Prove that B is a closed set

I'm new to all of this and just don't know what to do even with the f(x)=x²+2 part so if anyone out there can shed some light, I'd be really grateful!

Thanks

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# Functional analysis

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