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 19:44
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