(adsbygoogle = window.adsbygoogle || []).push({}); 1. a) Show that (f^-1 S)compliment = f^-1(S compliment) for any set S of reals.

Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.

2. inverse image = f^-1(S) = {x: f(x) [tex]\in[/tex] S}

f is continous iff for every open set U [tex]\in[/tex] the reals, f^-1(U) is open.

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# Homework Help: Inverse image and continuity

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