Abstract
The set B(X) of all nonempty bounded convex subsets of a topological vector space X endowed with the multiplication ⋆ given by: \(A \star B = A\dot + B\) and the ordering induced by the inclusion is an ordered commutative semigroup which satisfies the order cancellation law. The ordering as well as the multiplication can be extended to \({B^2}{\left( X \right)_{{/_\sim }}}\) by:
and
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© 2002 Springer Science+Business Media Dordrecht
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Pallaschke, D., Urbański, R. (2002). Fractions. In: Pairs of Compact Convex Sets. Mathematics and Its Applications, vol 548. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9920-7_11
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DOI: https://doi.org/10.1007/978-94-015-9920-7_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6149-2
Online ISBN: 978-94-015-9920-7
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