Math 131 120716 Ascoli Arzela And Stone Weierstrass

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Second part of proof (existence of uniformly convergent subsequence) of Take we know a plus c that is then so this is dense this is equal to this is closed and this is equal to c of x by Existence of uniformly convergent subsequences (i.e., sequential compactness with respect to the supremum norm metric).

Guide Summary

Existence of uniformly convergent subsequences (i.e., sequential compactness with respect to the supremum norm metric). Pointwise bounded sequence of functions on a countable set has a pointwise convergent subsequence (sketch).

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Important details found

• Second part of proof (existence of uniformly convergent subsequence) of
• Existence of uniformly convergent subsequences (i.e., sequential compactness with respect to the supremum norm metric).
• Pointwise bounded sequence of functions on a countable set has a pointwise convergent subsequence (sketch).
• Take we know a plus c that is then so this is dense this is equal to this is closed and this is equal to c of x by

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