mth536_problem_7_28b

mth536_problem_7_28b - MTH536 Chapter 7 Problem 28b Gene...

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Unformatted text preview: MTH536 Chapter 7 Problem 28b Gene Quinn – p. 1/ Chapter 7 Problem 28b If space ¡ ¢ is a uniformly continuous map of a totally bounded metric onto a metric space , then is totally bounded. ¥ ¥ ¥ £ £ Is this proposition true if continuous is substituted for uniformly continuous? ¤ – p. 2/ Proof of proposition In problem 23c, it was shown that total boundedness is not a topological property by establishing that defined by  ¡ ¢ ¨ © ¦§  ¤        ¨   ¦§  is a homeomorphism between the totally bounded space and , which is not totally bounded. Since a homeomorphism is continuous and onto, the result applies here. ¨ © ¦§    ¨ © ¦§  – p. 3/ ...
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mth536_problem_7_28b - MTH536 Chapter 7 Problem 28b Gene...

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