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

Exercise 4.8. For each of the following, state whether it is true 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 convex then 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.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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