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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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This note was uploaded on 10/18/2011 for the course MATH S4061X taught by Professor Peters during the Spring '11 term at Columbia.
 Spring '11
 Peters

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