Helly, Radon, and Carathéodory type theorems
J Eckhoff - Handbook of convex geometry, 1993 - Elsevier
Publisher Summary This chapter discusses applications and generalizations of the classical
theorems of Helly, Radon, and Carathéodory, as well as their ramifications in the context of
combinatorial convexity theory. These theorems stand at the origin of what is known today
as the combinatorial geometry of convex sets. Helly's theorem states that: letting K be a
family of convex sets in ℝ d, and supposing K is finite or each member of K is compact; if
every d+ 1 or fewer members of K have a common point, then there is a point common to all …
theorems of Helly, Radon, and Carathéodory, as well as their ramifications in the context of
combinatorial convexity theory. These theorems stand at the origin of what is known today
as the combinatorial geometry of convex sets. Helly's theorem states that: letting K be a
family of convex sets in ℝ d, and supposing K is finite or each member of K is compact; if
every d+ 1 or fewer members of K have a common point, then there is a point common to all …