Unformatted text preview: F ⊂ R , ﬁnd a sequence of reals { x n } whose set of subsequential limits is precisely F . Hint: Using homework 3, show that F is separable, when given the induced metric by R . Rudin, Ch3, problem 25 might be helpful. 7. [32] (5 points) Show that the Cantor set consists precisely of those points in [0 , 1] having a base3 expansion with no 1. Notice this gives an alternate proof that the Cantor set is uncountable! 1...
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 Spring '11
 Peters
 Metric space, Compact space, R. Rudin

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