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Homework Help: Help -interpreting- this topology question, no actual work required!

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the set S ⊆ C[0, 1] consisting of continuous functions which map Q to Q is dense, where the metric on C[0, 1] is defined by d(f,g) = max |f(x)−g(x)|.

    All else I need to know is what the question doesn't mention - what the set is dense in? I assume it doesn't mean dense in itself since it probably wouldn't bother giving a specific space then, so do you think it means the set of continuous R->R functions on [0,1] or all R->R functions on [0,1], or what? Just need to actually understand what it means before I can get going - thanks!
  2. jcsd
  3. Apr 27, 2009 #2


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    I'm sure they mean dense in C[0,1], the set of all continuous functions from [0,1]->R.
  4. Apr 27, 2009 #3
    Once again Dick, thanks for all the help, you're a lifesaver!
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