Characterizing sets of lower bounds: a hidden convexity result
The authors look for description of the set of lower bounds of a subset in an ordered vector space. Clearly, such a set \(C\) enjoys the following properties: (1) \(C\) is downward; (2) \(C\) is upper bounded; (3) \(C\) contains the supremum of its every subset that admits one. These conditions are proved to be sufficient in the case of a finite-dimensional space and a polyhedral positive cone. Simple counter-examples demonstrate the failure of the sufficiency in absence of polyhedrality.
scientific article; zbMATH DE number 6834679