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Questions tagged [semialgebraic-geometry]

Semialgebraic geometry is the study of semialgebraic sets. This tag is intended for problems in (or relating to) semialgebraic geometry and its generalizations: semianalytic, subanalytic, and o-minimal geometries. These areas have strong connections to logic via the Tarski-Seidenberg theorem, and solutions to problems in this tag often involve a mix of geometric and logical arguments.

Semialgebraic geometry is the study of semialgebraic sets. This tag is intended for problems in (or relating to) semialgebraic geometry and its generalizations: semianalytic, subanalytic, and o-minimal geometries. These areas have strong connections to logic via the Tarski-Seidenberg theorem, and solutions to problems in this tag often involve a mix of geometric and logical arguments.

64 questions
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Semi-algebraic neighbourhoods of a semi-algebraic set

Let $S\subset\mathbb{R}^n$ be a semi-algebraic set, and let $U\subset \mathbb{R}^n$ be an open neighbourhood of $S$ (non necessarily semi-algebraic). Is it true that there exists an open semi-algebraic neighbourhood $V\subset U$ of $S$? Is it true…
Antonio
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Stability under operations for semi algebraic functions

Let $E$ and $F$ two semialgebraic sets. Let $\phi(\alpha,\theta): E\times F$ a bounded semi-algebraic function. How to prove that $\theta\mapsto \sup_\alpha\phi(\alpha,\theta)$ is still semi-algebraic ? Have you some references where semi-algebraic…
peanpean
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Semialgebraic sets with irrational exponents

A semialgebraic set is defined by finite unions and complements of inequalities of the form $g(x)\ge 0$ where $g$ is a multivariate polynomial with integer coefficients. My question considers the extension of this to the case where $g$ might have…
Shaull
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Prove that infimum function is semi-algebraic by Tarski-Seidenberg theorem

I am reading the paper "A. D. Ioffe, An invitation to tame optimization, SIAM J. Optim., 19 (2009), 1894–1917" and stuck at Proposition 3.1. The author claims (in the language of semi-algebraic geometry) that if…
Dat Ba Tran
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