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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
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Helly's theorem in other areas of mathematics
The famous Krasnoselsky criteria for star-shaped regions is based on Helly theorem. It is important in embedding theorems for Sobolev spaces.
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A third degree surface and a touching sphere [closed]
Let consider a surface $z=1/(xy)$ and a sphere defined by $(x-1.5)^2+(y-1.5)^2+(z-1.5)^2=3/4$. The sphere touches the surface at (1,1,1). Is it possible to prove that point (1,1,1) is the only interse …