Metrics question

  • Thread starter thraxrules
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Can anyone prove this theorem please?
let (X,d) be a metric space, let [tex]x \in X[/tex] , and let [tex] 0<\delta<\epsilon [/tex]. Then cl(B(x,delta)) [tex] \subset [/tex]B(x,epsilon)
 
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  • #2
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Assume otherwise that is chose some y that is in the closure of B(x, eps) but is not in B(x, delt). Now use the triangle inequality that is required of the metric.
 

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