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Thread: Showing subspace is compact IFF any sequence of elements has a converging subsequece

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    Showing subspace is compact IFF any sequence of elements has a converging subsequece

    Show that a subspace X of the Euclidean space Rn is compact if and only if any
    sequence of elements of X has a converging subsequence. Remark: this statement
    holds in the considerably greater generality of any metric space but the proof of this
    more general result is quite involved.
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    Re: Showing subspace is compact IFF any sequence of elements has a converging subsequ

    Quote Originally Posted by Cloud141 View Post
    Show that a subspace X of the Euclidean space Rn is compact if and only if any
    sequence of elements of X has a converging subsequence. Remark: this statement
    holds in the considerably greater generality of any metric space but the proof of this
    more general result is quite involved.
    How do you define a combact subspace?
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