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Unformatted text preview: s , then s S . (a) Prove that, for any a,b R with a < b , that the interval [ a,b ] is closed. (b) Give two examples of an unbounded, closed set S R . Make sure to justify that your examples work. (c) Suppose that S R is a closed set that is bounded above. Prove that sup( S ) S . (d) A subset O R is said to be open if, for every x O , there is > 0 such that ( x,x + ) O . For example, any interval ( a,b ) is open. (You dont need to prove this; just convince yourself that this is true.) Prove, for a set S R , that S is closed if and only if R \ S is open....
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This note was uploaded on 01/30/2012 for the course MATH 131a taught by Professor Hitrik during the Spring '08 term at UCLA.
 Spring '08
 hitrik
 Math, Addition, Limits

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