Unformatted text preview: metric. Deﬁne 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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 Winter '11
 Wiley
 Differential Equations, Topology, Equations, Metric space, Closed set

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