Extending piecewise polynomial functions in two variables

DOI10.5802/afst.1372zbMath1279.14069OpenAlexW2322072686MaRDI QIDQ355221

Andreas Fischer, Murray A. Marshall

Publication date: 24 July 2013

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2013_6_22_2_253_0/

zbMATH Keywords

semi-algebraic setLipschitz conditiondefinable set\(o\)-minimal expansionlocal convexitypiecewise polynomial function

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Models of other mathematical theories (03C65)

Related Items (3)

Towards understanding the Pierce-Birkhoff conjecture via MV-algebras ⋮ A study of piecewise linear-quadratic programs ⋮ Characterization of Lipschitz normally embedded complex curves

Cites Work

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• Pierce-Birkhoff rings
• \(p\)-adic and real subanalytic sets
• On the Pierce-Birkhoff conjecture over ordered fields
• On the Pierce-Birkhoff conjecture in three variables
• o-minimal analytic separation of sets in dimension 2
• Lattice ordered rings and function rings
• Geometric categories and o-minimal structures
• O-minimal \(\Lambda ^{m}\)-regular stratification
• The Pierce-Birkhoff Conjecture for Curves
• Quasianalytic Denjoy-Carleman classes and o-minimality
• Continous, piecewise-polynomial functions which solve Hilbert's 17th problem.
• On the Pierce-Birkhoff conjecture

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