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somebody to help me, consider $\mathbb{Z}$ and $\mathbb{Q}$ as subspaces of $\mathbb{R}$ with the usual topology. The question is to show that every point of $\mathbb{Z}$ is isolated,and to show that no point of $\mathbb{Q}$ is isolated.

The definition for isolated point ; a point $x \in X$ is said to be isolated point of if the one -point set $\{x\}$ is open in $X$

THANKS!

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    Well, what makes a set open in the subspace topology? Can you show that a single point in the integers is open? What about the rationals? What have you tried so far, and where are you stuck?2011-05-31

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