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Real Analysis: closed sets and limit points

  1. Nov 14, 2013 #1
    For the following example:(if possible give example or just state impossible

    1) a bounded subset A of R for which sup A is not a limit point of A. An example is (0,1) union {7}. will this work?

    2) a finite subset A of R that is not closed
    I think it is not possible. Please give some hints if you think there is an answer
     
  2. jcsd
  3. Nov 14, 2013 #2

    Dick

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    1) works fine. For 2), can you think of a proof that nobody will be able to come up with an example?
     
    Last edited: Nov 14, 2013
  4. Nov 14, 2013 #3
    Wait ... why is ##7## not a limit point of ##(0,1)\cup\{7\}##?
     
  5. Nov 14, 2013 #4
    Since not all epilson nbhd of 7 intersects the subset other than 7 which violates the definition of limit
     
  6. Nov 15, 2013 #5
    If a set has no limit points, then by definition it is closed.
     
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