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Let $X=\{(p_1,p_2,\dots, p_n):p_i\in \mathbb Q\}$. Is $X $ connected or disconnected?

My attempt:$X$ is connected iff any two points of $X$ are contained in a connected subset of $X$. This attempt is Not working as it is difficult to find connected subsets of $X$. Would like to prove in this approach. Topology is usual topology of $\mathbb R^n$.

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    $\begingroup$ This question doesn't make sense unless we know what topology you're talking about. Are we considering $\mathbb Q$, $\mathbb R$, $\mathbb Q_p$...? $\endgroup$ – Joshua Mundinger Nov 7 '14 at 13:50
  • $\begingroup$ In particular, it's connected in $X$ under the indiscrete topology. $\endgroup$ – Joshua Mundinger Nov 7 '14 at 13:51
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Hint: consider the hyperplanes $x_i=k$, ($i$ fixed, $k\in\Bbb R\setminus\Bbb Q$).

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