Wagner, Sven
On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6 : Tome 19 (2010) no. S1 , p. 221-242
MR 2675729 | Zbl 1210.14069 | 1 citation dans Numdam
doi : 10.5802/afst.1283
URL stable : http://www.numdam.org/item?id=AFST_2010_6_19_S1_221_0

We will prove that the Pierce-Birkhoff Conjecture holds for non-singular two-dimensional affine real algebraic varieties over real closed fields, i.e., if W is such a variety, then every piecewise polynomial function on W can be written as suprema of infima of polynomial functions on W. More precisely, we will give a proof of the so-called Connectedness Conjecture for the coordinate rings of such varieties, which implies the Pierce-Birkhoff Conjecture.

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