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Topic: Convex subset
Replies: 21   Last Post: Dec 31, 2013 10:39 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Convex subset
Posted: Dec 5, 2013 12:16 AM
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A subset R, is convex when for all x,y in A, t in R,
if x < t < y, then t in A.

Assume f:[a,b] -> R is continuous.
Define g:[a,b] -> R by g(x) = sup f([a,x]).

Is g([a,b]) a convex subset of R.
How would that be proved?

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