
Convex subset
Posted:
Dec 5, 2013 12:16 AM


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?

