Brunner General Structures and Dependent Choice

Mihai Turinici ()
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Mihai Turinici: A. I. Cuza University, A. Myller Mathematical Seminar

Chapter 30 in Convex and Variational Analysis with Applications, 2026, pp 761-799 from Springer

Abstract: Abstract A general class of ordered metrical structures is introduced under the model in Brunner (Zeitschr Math Logik Grundl Math, 33:135–139, 1987). As a by-product of this, we show that the immense majority of all (sequential type) ordering/variational principles is nothing else than an equivalent version of the Bernays–Tarski Dependent Choice Principle.

Keywords: Ordered metric space; Ascending and bounded sequence; Maximal element; Lower semicontinuous function; Brunner general structure; Brezis-Browder Ordering Principle; Ekeland Variational principle; Equivalence; Dependent Choice Principle; 49J53 (Primary); 47J30 (Secondary) (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-07860-5_30

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