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Is there any application on the fact that $π_1(\mathbb{R}^2−\mathbb{Q}^2)$ is uncountable?

Rahman
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  • This post may have some of the information you want in its analysis. http://math.stackexchange.com/questions/16948/pi-1-mathbb-r2-mathbb-q2-is-uncountable – Ian Coley Mar 29 '13 at 23:03
  • Your further question baffles me... It is probably a useless piece of knowledge apart from the interesting fact that one can construct in suc a simple way such a complicated space. But what did you expect, really? Applications of that to what? – Mariano Suárez-Álvarez Mar 29 '13 at 23:04
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    usefulness.. maybe its good for proving something... – Rahman Mar 29 '13 at 23:06

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