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How do I show 6.2? Could you explain it in detail?

Theorem 6.2. Let C be a compact subset of Rstd- Then C has a maximum point, that is,
there is a point m E C such that for every x E C, x < m.
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Theorem 6.2. Let C be a compact subset of Rstd- Then C has a maximum point, that is, there is a point m E C such that for every x E C, x < m.

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