S20 - > > 0 such that | x n | > for innitely many...

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1st December 2004 Munkres § 20 Ex. 20.5. Consider R ω with the uniform topology and let d be the uniform metric. Let C R ω be the set of sequences that converge to 0. Then R = C. : Since clearly R C it is enough to show that C is closed. Let ( x n ) R ω - C be a sequence that does not converge to 0. This means that there is some 1
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Unformatted text preview: > > 0 such that | x n | > for innitely many n . Then B d (( x n ) , 1 2 ) R -C . : Let ( x n ) C . For any 1 > > 0 we have | x n | < for all but nitely many n . Thus B d (( x n ) , 2 ) R 6 = . References 1...
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This note was uploaded on 01/12/2011 for the course MATH 110 taught by Professor Brown during the Fall '08 term at Arizona Western College.

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