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there is a problem on topology.

Let $n > 1$ and let $X = \{(p_1,p_2, \ldots , p_n)\mid p_i\text{ is rational}\}$. Show that $X$ is disconnected.

how to solve this problem.i am completely stuck out.

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    By disconnected, do you mean "not connected", or "totally disconnected"? Both are true, but you'll need to approach it differently, depending on which you intend.2012-09-20
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    What is $i$? Do you mean that $p_1, p_2, \ldots p_n$ all have to be rational?2012-09-20
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    Please, try to make the titles of your questions more informative. E.g., *Why does $a imply $a+c?* is much more useful for other users than *A question about inequality.* From [How can I ask a good question?](http://meta.math.stackexchange.com/a/589/): *Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader.*2012-09-20
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    If the space $X$ is diconnected, then for all spaces $Y$ the product $X\times Y$ is also disconnected: this implies that it is enough to deal with the case $n=1$ of the problem.2012-09-20
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    What exactly are you stuck on? Start with the definition of connectedness (or totally disconnectedness), and look for results that would give you the conclusion you want. You can't be completely stuck on something that's this close to the definitions involved.2016-08-18

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