Could you explain how to show 6.17 in detail? The next theorem completely characterizes the sets in Rstd that are compact. Thistheorem, known as the Heine-Borel Theorem, is one of the fundamental theoremsabout the topology of the line.Recall a set A in R' is bounded if and only if there is a number M such that A C[-M, M].Theorem 6.15 (Heine-Borel Theorem). Let A be a subset of Rstd- Then A is compact ifand only if A is closed and bounded.Theorem 6.17. Every compact subset C of R contains a maximum in the set C, i.e., thereis an m E C such that for any x E C, x < m.

Name: Could you explain how to show 6.17 in detail? The next theorem complet
Uploaded: 2024-03-20T06:38:44.000Z
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Description: Could you explain how to show 6.17 in detail? The next theorem completely characterizes the sets in Rstd that are compact. Thistheorem, known as the Heine-Borel Theorem, is one of the fundamental theoremsabout the topology of the line.Recall a set A