Abstract
We will show that minimal pairs are not uniquely determined. However, in some special cases we are able to prove the uniqueness or at least some uniqueness properties. We begin with pairs of bounded closed convex sets which lie in complementary subspaces. Then we will consider minimal pairs of compact convex subsets in the plane. In this case the minimal pairs are uniquely determined up to translations. In spaces of higher dimension, this result is no longer true.
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© 2002 Springer Science+Business Media Dordrecht
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Pallaschke, D., Urbański, R. (2002). The Cardinality of Minimal Pairs. In: Pairs of Compact Convex Sets. Mathematics and Its Applications, vol 548. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9920-7_5
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DOI: https://doi.org/10.1007/978-94-015-9920-7_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6149-2
Online ISBN: 978-94-015-9920-7
eBook Packages: Springer Book Archive