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Math Help - A compact set contains in an open set...

  1. #1
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    A compact set contains in an open set...

    Problem: Let K be a compact subset in R^n. Suppose O is an open subset of R^n that contains K, prove there exists a postive number r such that Nr(u) equals to O for every u in K.

    My proof:

    .......

    I don't even know how to start...
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Problem: Let K be a compact subset in R^n. Suppose O is an open subset of R^n that contains K, prove there exists a positive number r such that Nr(u) equals to O for every u in K.
    Does the notation Nr(u) stand for a ball centered at u with radius r?
    If it does, and “Nr(u) equals to O for every u in K” is correctly written then the statement is false. However, if it reads “Nr(u) is a subset of O for every u in K” then that can be proved

    Please review and advise. Tell we us about the definitions.
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