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Math Help - open/closed sets

  1. #1
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    open/closed sets

    Well I guess this is not standard notation but here goes:

    Let A be a set in \mathbb{R}^n, then \partial A is the boundry of A.
    \overline{A}=A\cup\partial A
    and
    \overset{\circ}{A}=A\setminus\partial A

    Now prove that
    \overset{\circ}{\overset{\_}{\overset{\circ}{\over  set{\_}{A}}}}=\overset{\circ}{\overset{\_}{A}}

    and

    \overset{\_}{\overset{\circ}{\overset{\_}{\overset  {\circ}{A}}}}=\overset{\_}{\overset{\circ}{A}}

    I just have no idea how to do this one. Any hints greatly appriciated.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by hjortur View Post
    Well I guess this is not standard notation but here goes:

    Let A be a set in \mathbb{R}^n, then \partial A is the boundry of A.
    \overline{A}=A\cup\partial A
    and
    \overset{\circ}{A}=A\setminus\partial A

    Now prove that
    \overset{\circ}{\overset{\_}{\overset{\circ}{\over  set{\_}{A}}}}=\overset{\circ}{\overset{\_}{A}}

    and

    \overset{\_}{\overset{\circ}{\overset{\_}{\overset  {\circ}{A}}}}=\overset{\_}{\overset{\circ}{A}}

    I just have no idea how to do this one. Any hints greatly appriciated.
    I would just honestly try it. It isn't as ugly as it may appear. Let x be in the LHS and deduce that it's in the RHS. Come back if you need help.
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