Abstract
In this paper we generalize Robinson's version of an order cancellation law in which some unbounded subsets of a vector space are cancellative elements. We introduce the notion of weakly narrow sets in normed spaces, study their properties and prove the order cancellation law where the canceled set is weakly narrow. Also, we prove the order cancellation law for closed convex subsets of topological vector space where the canceled set has bounded Hausdorff-like distance from its recession cone. We topologically embed the semigroup of closed convex sets sharing a recession cone having bounded Hausdorff-like distance from it into a topological vector space. This result extends Bielawski and Tabor's generalization of Rådström theorem.
Acknowledgments
We would like to thank anonymous referees for valuable remarks that allowed us to improve the manuscript.
Citation
Jerzy Grzybowski. Hubert Przybycień. "Order Cancellation Law in a Semigroup of Closed Convex Sets." Taiwanese J. Math. 26 (6) 1281 - 1302, December, 2022. https://doi.org/10.11650/tjm/220603
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