ON THE SUBSTITUTION THEOREM FOR RINGS OF SEMIALGEBRAIC FUNCTIONS

DOI10.1017/S1474748014000206zbMath1330.14095arXiv1309.3743MaRDI QIDQ3192313

José F. Fernando

Publication date: 12 October 2015

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3743

zbMATH Keywords

semialgebraic setevaluation homomorphismssubstitution theoremextension of coefficientsring of bounded semialgebraic functionring of semialgebraic functionssemialgebraic pseudo-compactificationweak continuous extension property

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Semialgebraic sets and related spaces (14P10) Real-valued functions in general topology (54C30) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (4)

On Nash images of Euclidean spaces ⋮ On the remainder of the semialgebraic Stone-Čech compactification of a semialgebraic set ⋮ Continuous functions on the plane regular after one blowing-up ⋮ Spectral maps associated to semialgebraic branched coverings

Cites Work

• Characters on algebras of smooth functions
• Normal spectral spaces and their dimensions
• Homomorphisms on \(C^ \infty (E)\) and \(C^ \infty\)-bounding sets
• Real closed rings. II. Model theory
• Separation, retractions and homotopy extension in semialgebraic spaces
• Substitution in Nash functions
• A dimension theorem for real spectra
• Elementary properties of minimal and maximal points in Zariski spectra
• Finiteness problems on Nash manifolds and Nash sets
• Super real closed rings
• ON THE IRREDUCIBLE COMPONENTS OF A SEMIALGEBRAIC SET

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