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For questions involving the concept of convexity
7
votes
2
answers
313
views
Duality between extremal points and extremal maps
Suppose I have a convex set $C\subset\mathbb{R}^n$ such that $0\in C$ and every Cauchy sequence in $C$ converges in $C$, but $C$ need not be bounded. (Actually I want unbounded $C$). Consider the set …
2
votes
1
answer
353
views
Extensions of Carathéodory's theorem
We know about the Carathéodory's theorem which is on the convex bodies of $\mathbb{R}^d$. My question is, how far we can extend it? Is it true for say, any convex object of Banach space, or for convex …