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Why is the singular locus of a definable closed analytic set definable?

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#logic #model-theory #complex-geometry #semialgebraic-geometry
79
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Are the irreducible components of a definable closed analytic set themselves definable?

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#analytic-geometry #model-theory #complex-geometry #semialgebraic-geometry
151
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Why is the image of a subanalytic set through a proper analytic map subanalytic?

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#model-theory #analytic-functions #semialgebraic-geometry
215
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Closed semialgebraic subset of $\mathbb{R}^2$

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#algebraic-geometry #solution-verification #exponential-function #real-algebraic-geometry #semialgebraic-geometry
166
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Semialgebraic Morse-Sard Theorem - why are the critical points of a semi-algebraic map again semi-algebraic?

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#real-algebraic-geometry #semialgebraic-geometry
85
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Structure of Closed Semialgebraic set

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#real-algebraic-geometry #semialgebraic-geometry
119
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Semi-algebraic set has nonempty interior relative to Zariski closure

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#algebraic-geometry #real-algebraic-geometry #semialgebraic-geometry
156
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Semialgebraic set technical lemma

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#algebraic-geometry #real-algebraic-geometry #semialgebraic-geometry
167
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Product of semialgebraic sets is semialgebraic

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#real-algebraic-geometry #semialgebraic-geometry
281
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Dimension of a semialgebraic set equals the dimension of its closure.

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#algebraic-geometry #real-algebraic-geometry #semialgebraic-geometry
148
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Are these definitions of dimension for a real algebraic variety all equivalent?

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#algebraic-geometry #geometric-measure-theory #real-algebraic-geometry #semialgebraic-geometry
174
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The derivative of a semialgebraic map is semialgebraic

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#derivatives #algebraic-geometry #real-algebraic-geometry #semialgebraic-geometry
167
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Triangulation Theorem for semialgebraic maps

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#algebraic-geometry #real-algebraic-geometry #semialgebraic-geometry
63
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Nonnegativity of sparse polynomial with just one negative coefficient

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#inequality #polynomials #semialgebraic-geometry
33
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Prove that infimum function is semi-algebraic by Tarski-Seidenberg theorem

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#semialgebraic-geometry

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