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• W2899342008 abstract "Sets of lower bounds (also known as lower cuts), and sets with supremum, are characterized in the setting of Archimedean order-unit vector spaces (typically a Banach space ordered by means of a closed cone with non-empty interior). In this framework, our study proves that a set admits a supremum if and only if all the members of a newly defined family of supporting hyperplanes pass through a same point. This result is used to prove our second result. It states that a set is a lower cut if and only if it is bounded from above, downward, and contains the existing supremums of any of its subsets. As a consequence, we prove the following hidden convexity result: any set fulfilling the three above-mentioned conditions is necessarily a convex set." @default.
• W2899342008 created "2018-11-09" @default.
• W2899342008 creator A5019482376 @default.
• W2899342008 creator A5073026086 @default.
• W2899342008 date "2018-09-01" @default.
• W2899342008 modified "2023-09-27" @default.
• W2899342008 title "New representations of sets of lower bounds and of sets with supremum in Archimedean order-unit vector spaces" @default.
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• W2899342008 doi "https://doi.org/10.25431/11380_1167082" @default.
• W2899342008 hasPublicationYear "2018" @default.
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