suppose A is a linear order set with a copy of rationals in it that is $A=B\cup\{\bar{r}:r\in\mathbb{Q}\cap[0,1]\}$. is there an orde preserving map that preservs sup and inf betwwen A and $[0,1]$ in witch the image of $\bar{r}$ is $r$. for $[0,1]^2$ in witch the image of $\bar{r}$ is $(r,r)$ or $(0,r)$ who?
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closed as off topic by Goldstern, Ricky Demer, Pietro Majer, Asaf Karagila, Andy Putman Dec 2 '12 at 19:44Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 

