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Math Help - Interior, Closure and Boundary of sets

  1. #1
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    Interior, Closure and Boundary of sets

    A little topology (I think) problem here:

    For A:= [0,1) ∪ ([2,3] ∩ ) ∪ {5} ⊂ R (real numbers) find the closure, boundary and interior of A

    I know the definitions but I don't know how to actually calculate them
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  2. #2
    Super Member girdav's Avatar
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    Re: Interior, Closure and Boundary of sets

    To compute the closure, just notice that the closure of a finite union is the union of the closures.
    For the interior, can the points of \left[2,3\right]\cap \mathbb Q be in it? And what about \left\{5\right\}?
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    Re: Interior, Closure and Boundary of sets

    Quote Originally Posted by fylth View Post
    For A:= [0,1) ∪ ([2,3] ∩ ) ∪ {5} ⊂ R (real numbers) find the closure, boundary and interior of A
    Do you know that \overline{A\cup B}=\overline{A}\cup\overline{B}~?

    \overline{[0,1)}=[0,1],~\overline{[2,3]\cap\mathbb{Q}}=[2,3],~\&~\overline{\{5\}}=\{5\}
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  4. #4
    Super Member TheChaz's Avatar
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    Re: Interior, Closure and Boundary of sets

    The boundary is the closure toss (set difference) the set...
    The interior is...
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