Geometry of Subanalytic and Semialgebraic Sets: 150 (Progress in Mathematics) - Hardcover

Shiota, Masahiro

Hardcover

ISBN 10: 0817640002 ISBN 13: 9780817640002

Publisher: Birkhauser Boston Inc, 1997

Synopsis

Subanalytic and semialgebraic sets were introduced for topological and systematic investigations of real analytic and algebraic sets. This text aims to show that almost all known and unknown properties of subanalytic and semialgebraic sets follow abstractly from some fundamental axioms, and it aims to develop methods of proof that use finite processes instead of integration of vector fields. Although the proofs are elementary, the results are new and of interest to, for example, singularity theorists and topologists, and the new methods and tools developed provide a basis for further research by model theorists who apply model theory to geometry.

About this title

From the Back Cover

Subanalytic and semialgebraic sets were introduced for topological and systematic investigations of real analytic and algebraic sets. One of the author's purposes is to show that almost all (known and unknown) properties of subanalytic and semialgebraic sets follow abstractly from some fundamental axioms. Another is to develop methods of proof that use finite processes instead of integration of vector fields. The proofs are elementary, but the results obtained are new and significant - for example, for singularity theorists and topologists. Further, the new methods and tools developed provide solid foundations for further research by model theorists (logicians) who are interested in applications of model theory to geometry. A knowledge of basic topology is required.

Edition details

• Publisher: Birkhauser Boston Inc
• Publication date: 1997
• Language: English
• ISBN 10: 0817640002
• ISBN 13: 9780817640002
• Binding: Hardcover
• Number of pages: 352