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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?

  • 6
    $\{x\}$ and $\{y\}$ are only open relative to $\{x,y\}$ but not in $\mathbb R$.2012-04-27
  • 3
    (nor in $\mathbb Q$)2012-04-27

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