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$X$ is a metric space. $Y$ is a closed subset of $X$ such that the distance between any two points in $Y$ is at most $1$. Then 

  1. $Y$ is compact 
  2. Any continuous function from $Y \rightarrow \mathbb{R}$ is bounded 
  3. $Y$ is not an open subset of $X$ 
  4. none of the above
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