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Unformatted text preview: M T H 5 3 6 C h a p t e r 8 P r o b l e m 4 Gene Quinn – p. 1/ 4 Chapter 8 Problem 4 Prove that a mapping ¢ ¡ £ ¤ ¥ is continuous if and only if the inverse image of every closed set is closed. – p. 2/ 4 Proof of Proposition ¦ § Let ¨ © ¥ be an arbitr ar y closed subset of ¥ . Then ¥ ¨ is open. By h ypothesis , is contin uous , so ¥ ¨ © £ is open. – p. 3/ 4 Proof of Proposition ¦ § Let ¨ © ¥ be an arbitr ar y closed subset of ¥ . Then ¥ ¨ is open. By h ypothesis...
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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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