Let n>1 and let X={(p 1 ,p 2 ,…,p n )∣p i is rational} . Show that X is disconnected.
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Expert's answer
2012-10-05T08:00:47-0400
X is homeomorphic to product Q^n, where Q denotes rational numbers. Since q is disconnected, then product of disconnected spaces, will be also disconnected.
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