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Unformatted text preview: < ± that contains ∩ the Cantor set C = n N E n (deﬁned in Rudin 2.44). [ Hint : C ² E n , and each of the 2 n intervals in E n is contained in an open interval of length (1 + ± ) / 3 n ]. (b) Show that the Cantor set C ² R is compact. (not for credit) Show that the Cantor set is uncountable – either by ﬁxing the proof of Rudin 2.43, or by using another (e.g. diagonal) argument. MIT OpenCourseWare http://ocw.mit.edu 18.100B Analysis I Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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 Fall '10
 Prof.KatrinWehrheim
 Topology, Real Numbers, Sets, Metric space, Compact space

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