Any set of the form $\{x, y\}$ is disconnected. Wouldn't this imply that the rational numbers is a discrete space, since $\{x\}$ and $\{y\}$ are open?
The rational numbers are totally disconnected but not a discrete space?
3
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real-analysis
general-topology
connectedness
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6$\{x\}$ and $\{y\}$ are only open relative to $\{x,y\}$ but not in $\mathbb R$. – 2012-04-27
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3(nor in $\mathbb Q$) – 2012-04-27