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Unformatted text preview: metric. Dene d * ( x,y ) = min { 1 ,d ( x,y ) } . Verify that d * is a metric on S . Draw neighborhoods around the origin of radius 1 / 2, 1, and 2. 6. If A and B are compact subsets of a metric space ( X,d ), prove that A B is also compact. 7. Let x be a point in the metric space ( X,d ). Prove that the singleton set { x } is closed. 1...
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This note was uploaded on 10/16/2011 for the course MATH 34 taught by Professor Wiley during the Winter '11 term at UC Merced.
 Winter '11
 Wiley
 Differential Equations, Equations

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