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Math Help - Real analysis: Compact Sets

  1. #1
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    Real analysis: Compact Sets

    Here is the problem:


    I'm so hopelessly lost... Help Please!!!!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Phyxius117 View Post
    Here is the problem:


    I'm so hopelessly lost... Help Please!!!!
    A metric space is compact if and only if it's totally bounded and complete. I bet you know that \mathbb{Q} is not totally bounded (under the usual metric), \mathbb{Q}_{[0,1]} is not complete, \mathbb{R} is not totally bounded

    try d)

    Also, consider that in a metric space (or in a more general scenario) if x_n\to x then C=\{x\}\cup\left\{x_m:m\in\mathbb{N}\right\} is compact. See if that helps
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