I know that preimages are open for open images, since differentiability implies continuity. I suspect there is a counterexample to the above though. This is not homework, just study.
Answer
No. Consider $f(x)=x^2$ and the open interval $(-1,1)$.
I know that preimages are open for open images, since differentiability implies continuity. I suspect there is a counterexample to the above though. This is not homework, just study.
Answer
No. Consider $f(x)=x^2$ and the open interval $(-1,1)$.
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