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Unformatted text preview: M T H 5 3 6 C h a p t e r 7 P r o b l e m 2 3 d Gene Quinn p. 1/ 4 Chapter 7 Problem 23d Show that every totally bounded metric space is separable. p. 2/ 4 Proof that a totally bounded metric space is separable Suppose is a totally bounde d metr ic space . W e m ust sho w that has a countab le dense subset. The proposition is tr ivial if is finite or countab le , because then is closed and p. 3/ 4 Proof that a totally bounded metric space is separable Suppose is a totally bounde d metr ic space . W e m ust sho w that has a countab le dense subset. The proposition is tr ivial if is finite or countab le , because then is closed and Suppose is not countab l e . By h ypothesis , is totally bounded so f or an y giv en , there e xists a finite subset of such that f or e v er y there is an with ....
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This note was uploaded on 03/23/2010 for the course MATH 515 taught by Professor Staff during the Spring '08 term at Iowa State.
 Spring '08
 Staff

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