Constructible Sets in Real Geometry
Home > Mathematics and Science Textbooks > Mathematics > Geometry > Algebraic geometry > Constructible Sets in Real Geometry: (v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics)
Constructible Sets in Real Geometry: (v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics)

Constructible Sets in Real Geometry: (v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics)

|
     0     
5
4
3
2
1




Available


About the Book

This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be.

Table of Contents:
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.


Best Sellers


Product Details
  • ISBN-13: 9783540604518
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • Returnable: N
  • Weight: 550 gr
  • ISBN-10: 3540604510
  • Publisher Date: 23 May 1996
  • Binding: Hardback
  • Language: English
  • Series Title: v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics
  • Width: 155 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Constructible Sets in Real Geometry: (v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics)
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG -
Constructible Sets in Real Geometry: (v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Constructible Sets in Real Geometry: (v. 33 Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals

    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!