Question

Give an example of a continuous map f: R -->R and a closed subset B in R such that f(B) is not closed. Is this possible if B is bounded as well?
Please, help

Answer 1

I'm imagining that arctan(x) will satisfy this, since you can plug in all values but in the range you can't ever reach pi/2 or -pi/2.

Answer 2

Thank you very much.

Answer 3

How about \(f(x) =\dfrac{1}{x^2+1}\)?

Answer 4

I think if B =[ 0, infity) then f(x) = (0, 1] that works also, right?