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Thread: Proof - compact

  1. #1
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    Proof - compact

    A am revising for my exam and have come across a proof i'm struggling with as i struggle with prooofs involving compactness,

    If E is a subset of R^n Show that E is compact if and only if E is closed and bounded.

    I know this to be true but don't know how to prove it.

    Any help here would be greatly appreciated,

    Cheers
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  2. #2
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    Quote Originally Posted by monster View Post
    A am revising for my exam and have come across a proof i'm struggling with as i struggle with prooofs involving compactness,

    If E is a subset of R^n Show that E is compact if and only if E is closed and bounded.

    I know this to be true but don't know how to prove it.

    Any help here would be greatly appreciated,

    Cheers

    Too long to do it here, but it's completely standard. Google "Heine-Borel Theorem"

    Tonio
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