, Volume 118, Issue 1-2, pp 33-40

Some Erdös-Szekeres type results about points in space

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The Erdös-Szekeres convexn-gon theorem states that for anyn≥3, there is a smallest integerf(n) such that any set of at leastf(n) points in the planeE 2, no three collinear, contains the vertices of a convexn-gon. We consider three versions of this result as applied to convexly independent points and convex polytopes inE d >,d≥2.