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Math Help - Real Analysis-Compact Sets

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    Real Analysis-Compact Sets

    Show that if K is compact, then sup K and inf K both exist and are elements of K.
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    Quote Originally Posted by ajj86 View Post
    Show that if K is compact, then sup K and inf K both exist and are elements of K.
    Since K is bounded it has a supremum. But the supremum of K is a boundary point of K. However, K is closed and therefore it contains its boundary points. Therefore, K contains its supremum, and similarly its infimum.
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