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The title says it all, really. I'm confronted with this problem from my topology course, and I have made no progress. I'm not sure if I'm supposed to solve it with the "standard" topology on R or something else, but I think its true even with the "standard" topology- I just can't find such a function.

I would add that this is an introductory course in topology and I don't know most advanced notions.

ThighCrush
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  • Try with $f:\mathbb{R}\longrightarrow \mathbb{R}$ defined as $f(x):=1/x$ for $x\neq 0$ and $f(0)=1$. – user123043 Mar 29 '20 at 16:59
  • if I take the open interval ]-0.5,0.5[, the image would give me {1}U]-infinity,-2[U]2,infinity[, no? And this isn't open... – ThighCrush Mar 29 '20 at 17:05

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