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Math Help - Not compact by open cover

  1. #1
    Member thaopanda's Avatar
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    Not compact by open cover

    Show that the set S = { \frac{1}{n}: n \in N } is not compact by describing an open cover of it that does not have a finite cover.

    any help appreciated!
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  2. #2
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    Quote Originally Posted by thaopanda View Post
    Show that the set S = { \frac{1}{n}: n \in N } is not compact by describing an open cover of it that does not have a finite cover.
    What about O_n=\left(\frac{1}{n+1},2\right)?
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  3. #3
    Member thaopanda's Avatar
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    I don't really understand what you mean by that question...
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    Quote Originally Posted by thaopanda View Post
    I don't really understand what you mean by that question...
    Is the collect \left\{ {O_n } \right\} such a cover?
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  5. #5
    Member thaopanda's Avatar
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    does it have to be n+1? doesn't H = { A_n} where A_n = (\frac{1}{n},2) work? H being the open cover with no finite subcover.
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