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Math Help - Is this open cover example correct?

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    Is this open cover example correct?

    I need to find an open cover of {x: x>0} with no finite subcover. Is this one?

    x \in(0,1) and O_x=(x/2,1)
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tn11631 View Post
    I need to find an open cover of {x: x>0} with no finite subcover. Is this one?

    x \in(0,1) and O_x=(x/2,1)
    Why is it even an open cover?

    How about \left\{(n,n+1):n\in\mathbb{N}\cup\{0\}\right\}\cup  \left\{B_1(n):n\in\mathbb{N}\right\}?
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    Quote Originally Posted by Drexel28 View Post
    Why is it even an open cover?

    How about \left\{(n,n+1):n\in\mathbb{N}\cup\{0\}\right\}\cup  \left\{B_1(n):n\in\mathbb{N}\right\}?
    oh, ok. I get it now. Thank you.
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    Quote Originally Posted by tn11631 View Post
    I need to find an open cover of {x: x>0} with no finite subcover.
    Frankly, a simple answer is best.
    It did ask for an open covering: \left\{ {\left( {\frac{1}{n},\infty } \right):\,n \in \mathbb{Z}^ +  } \right\}.
    This makes it very clear the you understand the thrust of the question.
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