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Proof of an equality

  1. Oct 15, 2011 #1
    Let A be a metric space and B be a compact subset of A.
    Is it true that an equality B = Int(B) [itex]\cup[/itex] bd(B) holds??
     
  2. jcsd
  3. Oct 15, 2011 #2

    HallsofIvy

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    In a metric space every compact set is closed (actually in every topological space). What does that tell you about its boundary points?
     
  4. Oct 15, 2011 #3
    Boundary point is also limit point, right?
    Then it belongs to B since B is closed?
     
  5. Oct 15, 2011 #4
    Hausdorff topological space, no? Which does include metric spaces, I admit.
     
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