Where do I read about semi-algebraic/analytic sets?

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Asked 8 years, 9 months ago

Modified 6 years, 9 months ago

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What's a good introduction to semi-algebraic/semi-analytic sets?

I'm coming from algebraic geometry, so ideally I'd prefer material that has a similar point of view and highlights analogies.

I've seen the wikipedia pages https://en.wikipedia.org/wiki/Semialgebraic_set and https://en.wikipedia.org/wiki/Subanalytic_set and the references there. I thought I'd ask here, before plunging into them.

asked Dec 7, 2015 at 21:33

Mattia Talpo

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$\begingroup$ amazon.com/Lectures-Real-Geometry-Societies-Transition/dp/… $\endgroup$
– pro
Commented Dec 7, 2015 at 21:44
8

$\begingroup$ certainly, Bochnak, Jacek; Coste, Michel; Roy, Marie-Françoise. Real Algebraic Geometry. Translated from the 1987 French original. Revised by the authors. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 36. Springer-Verlag, Berlin, 1998. x+430 pp $\endgroup$
– Dima Pasechnik
Commented Dec 7, 2015 at 21:56
4

$\begingroup$ and this: perso.univ-rennes1.fr/michel.coste/polyens/SAG.pdf $\endgroup$
– Dima Pasechnik
Commented Dec 7, 2015 at 22:01
$\begingroup$ Thanks (to both)! If you'd like to write your suggestions as an answer, I'll accept it if nobody writes anything more detailed... $\endgroup$
– Mattia Talpo
Commented Dec 8, 2015 at 6:44
2

$\begingroup$ You can also look at Claus Scheiderer's survey "Positivity and sums of squares: A guide to recent results" $\endgroup$
– user94803
Commented Jul 7, 2016 at 13:00

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