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Unformatted text preview: x by x = d 1 3 + d 2 9 + d 3 27 + ··· + d n 3 n + ··· = ∞ X k =1 d k 3 k , where d k ∈ { , 1 , 2 } . Then the Cantor set consists of exactly those x ∈ [0 , 1] which have d k ∈ { , 2 } , ∀ k . § 3.2.3 Exercise: #1,4,7,8,13 Recommended: #2,5,14 #7,13 are shortanswer. 1. Suppose U is open, C is closed, and K is compact. (a) Is U \ C open? Is C \ U closed? (b) Is U \ K open? Is C \ K compact? 52 Math 413 Topology of the Real Line (c) If V is open, can U \ V be open? (d) If J is compact, can K \ J be compact? 2. Prove the theorems about the Cantor set, using whichever of the deﬁnitions seems best....
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 Fall '11
 Wong
 Sets

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