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Limit pts check

  1. Oct 15, 2008 #1
    Could somebody throw their hat in with me on these?

    a. [tex]\{1- \frac{(-1)^n}{n}:n \in \mathbb{N} \}[/tex]

    Limit point = 1 , Isolated points are equal to the whole set

    b. [tex]\{ (-1)^n + \frac{1}{n} : n \in \mathbb{N} \} [/tex]

    Limit points are -1 and 1, Isolated points are the whole set

    c. [tex](0,1) \cup 2[/tex]

    Limit points are [0,1], Isolated point is 2.

    d. [tex] \mathbb{N} [/tex]

    Limit points none, Isolated points are [tex]\mathbb{N}[/tex]

    e. [tex] \mathbb{R} \backslash \mathbb{Q}[/tex]

    Limit points are [tex]\mathbb{R}[/tex], Isolated points are none.

    f. [tex] \mathbb{Q} \cap (0,1) [/tex]

    Limits points are [0,1], Isolated points are none
     
    Last edited: Oct 15, 2008
  2. jcsd
  3. Oct 16, 2008 #2

    morphism

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    If by limit/isolated points you mean limit/isolated points in R with its usual topology, then I agree with what you have.
     
  4. Oct 16, 2008 #3
    Yes, thanks morphism.

    I meant usual topology and R1. thanks
     
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