Let an R-body be the complement of the union of open balls of radius R in the Euclidean space. 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.
On the complements of union of open balls of fixed radius in the euclidean space / Marco Longinetti, Paolo Manselli, Adriana Venturi. - In: LE MATEMATICHE. - ISSN 2037-5298. - ELETTRONICO. - LXXVIII:(2023), pp. 3-22. [10.4418/2023.78.1.1]
On the complements of union of open balls of fixed radius in the euclidean space
Marco Longinetti;Paolo Manselli;Adriana Venturi
2023
Abstract
Let an R-body be the complement of the union of open balls of radius R in the Euclidean space. 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.
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
