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Question: Find all connected and path-connected subsets of $\mathbb{Q}$

We've shown that the connected subsets of $\mathbb{Q}$ are all sets that contain exactly one element of $\mathbb{Q}$.

Now our reasoning is as follows: Since path-connected subsets of $\mathbb{Q}$ are connected as well, all path-connected subsets of $\mathbb{Q}$ are only the single-element subsets as well.

Is this reasoning correct?

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    That was quick. Thanks :)2012-06-01

1 Answers 1

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Yes.