On the complements of union of open balls of fixed radius in the Euclidean space

  • M. Longinetti University of Firenze, Italy
  • P. Manselli University of Firenze, Italy
  • A. Venturi University of Firenze, Italy


Let an R-body be the complement of the union of open balls of radius R in Ed . The R-hulloid of a closed not empty set A, the minimal R-body containing A, is investigated; if A is the set of the vertices of a simplex, the R-hulloid of A is completely described (if d = 2) and if d > 2 special examples are studied. The class of R-bodies is compact in the Hausdorff metric if d = 2, but not compact if d > 2.