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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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- Spring '08
- Topology, Metric space, Uniform continuity, Gene Quinn, uniformly continuous map, uniform homeomorphism preserves