Let $D^n$ be the closed unit ball in $\mathbb{R}^n$. Given a compact, $n$-dimensional, AR(Absolute Retract) metric space $X$, must it happen that either $X$ embeds in $D^n$ or $D^n$ embeds in $X$?
Thank you
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$\begingroup$ ?? -- make your ball big enough. $\endgroup$– Włodzimierz HolsztyńskiCommented Apr 1, 2015 at 8:43
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$\begingroup$ @Włodzimierz Holsztyński I do not understand your comment, in general $X$ does not embeds in $\mathbf{R}^n$. Could you explain what do you mean? $\endgroup$– Pedro PerezCommented Apr 1, 2015 at 14:44
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$\begingroup$ My mistake, sorry (I assumed--wrongly--that $\ X\subseteq\mathbb R^n$). $\endgroup$– Włodzimierz HolsztyńskiCommented Apr 1, 2015 at 19:35
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$\begingroup$ There are plenty of the requested examples. Karol Borsuk had a paper in dimension $\ 2\ $ with a more advanced goal. The paper was presented during the first topological conference in Prague, during the summer of 1961. And it was published in the conference proceedings. $\endgroup$– Włodzimierz HolsztyńskiCommented Apr 1, 2015 at 19:38
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$\begingroup$ @Włodzimierz Holsztyński The paper contains counterexamples? Could you give more details about the paper of Borsuk? Thanks! $\endgroup$– Pedro PerezCommented Apr 1, 2015 at 20:31
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