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Math Help - Open sets and closed sets

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    Open sets and closed sets

    Explain why, if U is open and H is closed, then the set U \ H must be open.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Slazenger3 View Post
    Explain why, if U is open and H is closed, then the set U \ H must be open.
    Because, whatever definition of open you're using we have that H is closed means H' is open, and so U-H=U\cap H' which is the intersection of two open sets...which is...open!
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