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Compactness of a space

  1. Aug 18, 2009 #1
    I am considering the set of all bounded signals given by

    [tex] X = \left\{ x:\ |x(t)| \leq X_{\max}, \forall t \right\}.[/tex]

    Is this set compact? Can anyone help me?

    Thank you guys
     
  2. jcsd
  3. Aug 19, 2009 #2

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    No, bounded alone does not imply compact
    (in the topology of uniform convergence).
     
  4. Aug 19, 2009 #3
    in what topology, in what space of functions ?
     
  5. Aug 19, 2009 #4

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    He said signals, so I guess it's something like periodic functions
    that are a.e. C^1.
     
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