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Answer to Question #15805 in Abstract Algebra for ran
Question #15805
Let n>1 and let X={(p 1 ,p 2 ,…,p n )∣p i is rational} . Show that X is disconnected.
Expert's answer
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.
disconnected, then product of disconnected spaces,
will be also disconnected.
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