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Given a set $X$, define a function $d:X\times X\rightarrow \mathbb{R}$ by $d(x,y) = 1$ if $x\neq y$ and $d(x,y)=0$ if $x=y$. Show that the metric topology on $X$ is equal to the discrete topology.

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    What a discrete hint!2011-04-30
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    The title does not reflect the question.2011-04-30

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