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Math Help - Compactness and sequentiall compactness

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    Compactness and sequentiall compactness

    is there a difference between compactness and sequential compactness in a metric space or are these two terms simply interchangable?
    From what i can understand sequentially compact means that every subsequence has a convergent subsequence within the space and compact is the topological definition with repsect to subcovers which i have read twenty times but have no idea what it means. Can anyuone clarify?
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    Re: Compactness and sequentiall compactness

    Quote Originally Posted by johnnys View Post
    is there a difference between compactness and sequential compactness in a metric space or are these two terms simply interchangable? Sequentially compact means that every subsequence has a convergent subsequence within the space and compact is the topological definition with repsect to subcovers which i have read twenty times but have no idea what it means. Can anyuone clarify?
    In a metric space sequentially compactness is equivalent to compactness.
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