# 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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