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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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Can the intersection of the boundaries of compact and convex sets be a single element?
Let $H_1,H_2,\dots,H_n$ be compact and convex sets in $\mathbb{R}^n$ such that $\bigcap_{j=1}^n H_j$ has non-empty interior and for each $i=1,2,\dots,n$ there exist at least one element $x \in H_i$ su …