Unformatted text preview: x ∈ E and y ∈ E c . They are connected by the segment [ x , y ] := { x ( t ) := x + t ( yx ) : 0 ≤ t ≤ 1 } in R n . Finally, consider the point z := x ( t ) , where t := sup { t ∈ [0 , 1] : x ( t ) ∈ E } . In the remaining two problems, the following notations are used: A c := R n \ A, o Athe interior of A, Athe closure of A. #4. For an arbitrary set E ⊂ R n , show that ( o E ) c = E c . #5. Denote o E the interior of E , E the closure of E , o E the interior of E , etc. Give examples of sets E such that: (a) o E 6 = o o E , (b) E 6 = o E....
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This note was uploaded on 02/15/2012 for the course MATH 8601 taught by Professor Staff during the Fall '08 term at Minnesota.
 Fall '08
 Staff
 Math

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