Geometry of subanalytic and semialgebraic sets
By: Masahiro Shiota.
Series: Progress in mathematics -- vol. 150
Publisher: Birkhäuser; Birkhäuser Boston
Published: 1997
Place of publication: Boston
Language: eng
Number of pages: 431
Subjects: Semialgebraic sets.; Semianalytic sets.
Description: 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.
Notes: Includes bibliographical references (p. [421]-424) and index.