Dedekind-complete

Dedekind-complete

Dedekind-complete refers to a property of a vector lattice where every nonempty subset that is bounded from above has a supremum and every nonempty subset that is bounded from below has an infimum. In other words, a vector lattice is Dedekind-complete if every nonempty upper or lower order bounded subset has a supremum or infimum, respectively, within the lattice.From: Sequence Space Theory with Applications [2023], Semicontinuity of the minimal solution mappings to parametric set optimization problems on Banach lattices [2023]

Hahn-Banach and Duality Type Theorems for Vector Lattice-Valued Operators and Applications to Subdifferential Calculus and Optimization

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Published in S. A. Mohiuddine, Bipan Hazarika, Sequence Space Theory with Applications, 2023

Antonio Boccuto

We recall the construction of an integral for functions taking values in an arbitrary Dedekind complete vector lattice R, with respect to finitely additive positive real-valued set functions, which is inspired by a technique due to W. Chojnacki (see, e.g., [29]).

Semicontinuity of the minimal solution mappings to parametric set optimization problems on Banach lattices

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Published in Optimization, 2023

Yu Han, Kai Zhang

Let be a partially ordered set. is said to be order complete, if every nonempty subset of X has a supremum and an infimum. is said to be Dedekind complete, if every nonempty subset which is bounded from above has a supremum and every nonempty subset which is bounded from below has an infimum.

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Hahn-Banach and Duality Type Theorems for Vector Lattice-Valued Operators and Applications to Subdifferential Calculus and Optimization

Semicontinuity of the minimal solution mappings to parametric set optimization problems on Banach lattices