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Exercise 4.8. For each of the following, state whether it is true or false. If true, prove....

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Advance Math

Exercise 4.8. For each of the following, state whether it istrue or false. If

true, prove. If false, provide a counterexample.
(i) LetX beasetfromRn. ThesetX isclosedifandonlyifX isconvex.

(ii) Let X and Y be sets from Rn. If X ?Y is closed and convexthen Xand Y are both closed and convex sets.

(iii) LetX beanopensetandY ?X. IfY =??,thenY isaconvexset.

(iv) SupposeX isanopensetandY isaconvexset. IfX?Y ?X then

X?Y isopen.

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