Title: Estimates for the minimal width of polytopes inscribed in convex bodies
Abstract: The paper deals with the problem of approximating point sets byn-point subsets with respect to the minimal widthw. Let, in particular, ℋ d denote the family of all convex bodies in Euclideand-space, letA ⊂ ℋ d and letn be an integer greater thand. Then we ask for the greatest number μ=Λ n (A) such that everyA εA contains a polytope withn vertices which has minimal width at least μw(A). We give bounds for Λ n (ℋ d ), for Λ n (ℳ2133; d ), and for Λ n (W d ), where ℳ2133; d ,W d denote the families of centrally symmetric convex bodies and of bodies of constant width, respectively.