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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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 Spring '08
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