ArticleOriginal scientific text
Title
Minimality in asymmetry classes
Authors 1
Affiliations
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Abstract
We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].
Keywords
convex sets, symmetry, minimality, Hausdorff metric
Bibliography
- J. Grzybowski, Minimal pairs of convex compact sets, Arch. Math. (Basel) 63 (1994), 173-181.
- D. Pallaschke, S. Scholtes and R. Urbański, On minimal pairs of convex compact sets, Bull. Polish Acad. Sci. Math. 39 (1991), 1-5.
- R. Schneider, On asymmetry classes of convex bodies, Mathematika 21 (1974), 12-18.
- G. C. Shephard and G. Ewald, Normed vector spaces consisting of classes of convex sets, Math. Z. 91 (1966), 1-19.
- R. Urbański, A generalization of the Minkowski-Rådström-Hörmander Theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 709-715.
Pages:
149-154
Main language of publication
English
Received
1996-05-23
Accepted
1996-12-12
Published
1997
Exact and natural sciences