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Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Constructible Sets in Real Geometry ([EBook] /) / by Carlos Andradas, Ludwig Bröcker, Jesús M. Ruiz.
Author	Andradas, Carlos
Added Personal Name	Bröcker, Ludwig author.
Added Personal Name	Ruiz, Jesús M. author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg, , 1996.
Physical Details	IX, 270 p. : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 0071-1136 ; ; 33
ISBN	9783642800245
Contents note	I. A First Look at Semialgebraic Geometry -- 1. Real Closed Fields and Transfer Principles -- 2. What is Semialgebraic Geometry? -- 3. Real Spaces -- 4. Examples -- II. Real Algebra -- 1. The Real Spectrum of a Ring -- 2. Specializations, Zero Sets and Real Ideals -- 3. Real Valuations -- 4. Real Going-Up and Real Going-Down -- 5. Abstract Semialgebraic Functions -- 6. Cylindrical Decomposition -- 7. Real Strict Localization -- Notes -- III. Spaces of Signs -- 1. The Axioms -- 2. Forms -- 3. SAP-Spaces and Fans -- 4. Local Spaces of Signs -- 5. The Space of Signs of a Ring -- 6. Subspaces -- Notes -- IV. Spaces of Orderings -- 1. The Axioms Revisited -- 2. Basic Constructions -- 3. Spaces of Finite Type -- 4. Spaces of Finite Chain Length -- 5. Finite Type = Finite Chain Length -- 6. Local-Global Principles -- 7. Representation Theorem and Invariants -- Notes -- V. The Main Results -- 1. Stability Formulae -- 2. Complexity of Constructible Sets -- 3. Separation -- 4. Real Divisors -- 5. The Artin-Lang Property -- Notes -- VI. Spaces of Signs of Rings -- 1. Fans and Valuations -- 2. Field Extensions: Upper Bounds -- 3. Field Extensions: Lower Bounds -- 4. Algebras -- 5. Algebras Finitely Generated over Fields -- 6. Archimedean Rings -- 7. Coming Back to Geometry -- Notes -- VII. Real Algebra of Excellent Rings -- 1. Regular Homomorphisms -- 2. Excellent Rings -- 3. Extension of Orderings Under Completion -- 4. Curve Selection Lemma -- 5. Dimension, Valuations and Fans -- 6. Closures of Constructible Sets -- 7. Real Going-down for Regular Homomorphisms -- 8. Connected Components of Constructible Sets -- Notes -- VIII. Real Analytic Geometry -- 1. Semianalytic Sets -- 2. Semianalytic Set Germs -- 3. Cylindrical Decomposition of Germs -- 4. Rings of Global Analytic Functions -- 5. Hilbert’s 17th Problem and Real Nullstellensatz -- 6. Minimal Generation of Global Semianalytic Sets -- 7. Topology of Global Semianalytic Sets -- 8. Germs at Compact Sets -- Notes.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-80024-5
Links to Related Works	Subject References: Algebraic Geometry . Mathematics . Authors: Andradas, Carlos . Bröcker, Ludwig . Ruiz, Jesús M. . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics . Classification: 516.35 .

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Constructible Sets in Real Geometry

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