Minimality in asymmetry classes
Studia Mathematica (1997)
- Volume: 124, Issue: 2, page 149-154
- ISSN: 0039-3223
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topWiernowolski, Michał. "Minimality in asymmetry classes." Studia Mathematica 124.2 (1997): 149-154. <http://eudml.org/doc/216403>.
@article{Wiernowolski1997,
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].},
author = {Wiernowolski, Michał},
journal = {Studia Mathematica},
keywords = {convex sets; symmetry; minimality; Hausdorff metric; convex set; topological vector space; Rådström-Hörmander lattice},
language = {eng},
number = {2},
pages = {149-154},
title = {Minimality in asymmetry classes},
url = {http://eudml.org/doc/216403},
volume = {124},
year = {1997},
}
TY - JOUR
AU - Wiernowolski, Michał
TI - Minimality in asymmetry classes
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 2
SP - 149
EP - 154
AB - 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].
LA - eng
KW - convex sets; symmetry; minimality; Hausdorff metric; convex set; topological vector space; Rådström-Hörmander lattice
UR - http://eudml.org/doc/216403
ER -
References
top- [1] J. Grzybowski, Minimal pairs of convex compact sets, Arch. Math. (Basel) 63 (1994), 173-181. Zbl0804.52002
- [2] D. Pallaschke, S. Scholtes and R. Urbański, On minimal pairs of convex compact sets, Bull. Polish Acad. Sci. Math. 39 (1991), 1-5. Zbl0759.52003
- [3] R. Schneider, On asymmetry classes of convex bodies, Mathematika 21 (1974), 12-18. Zbl0288.52003
- [4] G. C. Shephard and G. Ewald, Normed vector spaces consisting of classes of convex sets, Math. Z. 91 (1966), 1-19. Zbl0141.39003
- [5] R. Urbański, A generalization of the Minkowski-Rådström-Hörmander Theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 709-715. Zbl0336.46009
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