Order Cancellation Law in a Semigroup of Closed Convex Sets

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...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2022-12, Vol.26 (6), p.1281-1302
Main Authors: Grzybowski, Jerzy, Przybycień, Hubert
Format: Article
Language:English
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Summary: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.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/220603