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Let $\mathbb R_{\ell}$ be the real line equipped with the lower limit topology and $\mathbb R_u$ be the real line equipped with the upper limit topology. Which of the following functions is a homeomorphism $\mathbb R_{\ell}\rightarrow\mathbb R_u$?

A

$f(x)=0$

B

$f(x)=x$

C

$f(x)=-x$

D

$f(x)=x^3$

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