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Open sets and compact sets

  1. Nov 2, 2009 #1
    Is it true that every open set contains a compact set?
     
  2. jcsd
  3. Nov 2, 2009 #2
    Well, the empty set is open. And yes, even the empty set contains a compact set.
     
  4. Nov 3, 2009 #3

    HallsofIvy

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    Showing that one open set contains a compact set does not prove what the OP wanted!

    However, I can finish by showing the "easy" part: If A is not empty, then it contains, say, "a". The singleton set "a", since it is finite, is compact.
     
  5. Nov 3, 2009 #4
    My point was, that every open set contains the empty open set, which contains the empty compact set. So I was not really doing *one* open set after all.
     
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