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Unformatted text preview: in S as well as points not in S : B ( x ) S n = , but B ( x ) n S. The set of boundary points of S is called the boundary and denoted S . The following are relatively easy observations (Exercise 10 ): Remark 3.6.9. 1. For any set S R 3 , S int S S. 2. The boundary S of any set is closed. 3. S is closed precisely if it contains its boundary points: S closed S S. 4. S R 3 is closed precisely if its complement R 3 \ S := { x R 3  x / S } is open ....
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 Fall '08
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 Calculus, Sets

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