mth536_problem_7_23a

Mth536_problem_7_23a - M T H 5 3 6 C h a p t e r 7 P r o b l e m 2 3 a Gene Quinn – p 1 4 Chapter 7 Problem 23a Show that boundedness is a metric

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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 a Gene Quinn – p. 1/ 4 Chapter 7 Problem 23a Show that boundedness is a metric but not a uniform property. – p. 2/ 4 Proof of proposition The proposition will be estab lished if w e can produce a unif or m homeomor phism betw een a bounde d metr ic space and one that is not bounded . – p. 3/ 4 Proof of proposition The proposition will be estab lished if w e can produce a unif or m homeomor phism betw een a bounde d metr ic space and one that is not bounded . Let ¡£ ¢ ¤ ¥ be the set ¡ ¦ § ¨ ¢ © equipp ed with the metr ic ¤ ¢ ¦ Clear ly ¢ ¡ can be chosen to mak e ¤ ¢ larger than an y preassigned v alue , so ¡ ¢ ¤ ¥ is not a bounde d metr ic space . – p. 3/ 4 Proof of proposition The proposition will be estab lished if w e can produce a unif or m homeomor phism betw een a bounde d metr ic space and one that is not bounded ....
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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.

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Mth536_problem_7_23a - M T H 5 3 6 C h a p t e r 7 P r o b l e m 2 3 a Gene Quinn – p 1 4 Chapter 7 Problem 23a Show that boundedness is a metric

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