Sortov convergence
This week's homework from the Sortov Institute is only mildly
eccentric.
Let (x_n)_{n\in N} be a sequence of elements of R^2 such that the
convex hull of the trio
{x_n , x_{n+1} , x_{n+2} }
contains the point x_{n+3}, for every n. Show that the subsequences
(x_{3n})
(x_{3n+1})
(x_{3n+2})
are convergent.
.
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