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Let $f : X \rightarrow Y$ be a continuous map between metric spaces. Then $f(X)$ is a complete subset of $Y$ if 

  1. The space $X$ is compact 
  2. The space $Y$ is compact 
  3. The space $X$ is complete 
  4. The space $Y$ is complete.
in Linear Algebra by Boss (29.6k points) | 59 views

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