mth536_problem_7_28a

mth536_problem_7_28a - MTH536 Chapter 7 Problem 28a Gene...

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Unformatted text preview: MTH536 Chapter 7 Problem 28a Gene Quinn – p. 1/ Chapter 7 Problem 28a Show that if is a uniformly continuous map of a totally bounded metric space onto a metric space , then is totally bounded. ¡ ¢ £ ¤ ¥ £ ¥ ¥ – p. 2/ Proof of proposition In problem 23b, we established that a uniform homeomorphism preserves total boundedness. However, the proof used only the uniform continuity of and the fact that was onto, so it applies here as well. – p. 3/ ...
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mth536_problem_7_28a - MTH536 Chapter 7 Problem 28a Gene...

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