Unformatted text preview: in S as well as points not in S : B ε ( −→ x ) ∩ S n = ∅ , but B ε ( −→ 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 ....
View
Full Document
 Fall '08
 ALL
 Calculus, Sets, Interior, General topology, Boundary, Bε

Click to edit the document details