The Szökefalvi-Nagy Problem
Let M ⊂ R n be a compact, convex body. We consider the family T(M) of all its translates (Fig. 111) and denote by him M the Helly dimension of T(M): him M = him T(M). This chapter is devoted to the Helly-dimensional classification of compact, convex bodies. In other words, we are going to consider the following problem: to give a geometrical description of the compact, convex bodies M ⊂ R n satisfying him M = r, where 1 ≤ r ≤ n. By reasons which will be mentioned in this section, this problem is said to be the Szökefalvi-Nagy problem.
KeywordsConvex Body Vector System Nonzero Vector Direct Decomposition Symmetric Body
Unable to display preview. Download preview PDF.