Subanalytic sets à la polonaise. With an introduction to analytic functions and sets. With a preface by Bernard Teissier. (Ensembles sous-analytiques à la polonaise. Avec une introduction aux fonctions et ensembles analytiques.) (French) Zbl 1153.32011
Travaux en Cours 69. Paris: Hermann, Éditeurs des Sciences et des Arts (ISBN 978-2-7056-6688-0/pbk). viii, 121 p. (2007).
The book presents the theory of subanalytic sets as it was developed by S. Łojasiewicz during the years 1979–1984. It starts with a brief introduction into the theory of analytic functions and analytic sets; real and complex.
Then, the first chapter introduces normal partitions. The second chapter contains preliminaries on subanalytic sets. The third part of the book is dedicated to metric properties of subanalytic sets like: regular separation, Whitney property and the decomposition of a subanalytic set as graphs of analytic functions with bounded derivatives.
The fourth chapter is about fiber properties of a subanalytic set. Chapter 5 studies subanalytic stratifications and Whitney stratifications. The last part of the book, Chapter 6, on regular points and Nash points, proves the main theorem of this section, namely, the subanalyticity of the set of singular points of a subanalytic set.
The book suits well for graduate students and young researchers.
Then, the first chapter introduces normal partitions. The second chapter contains preliminaries on subanalytic sets. The third part of the book is dedicated to metric properties of subanalytic sets like: regular separation, Whitney property and the decomposition of a subanalytic set as graphs of analytic functions with bounded derivatives.
The fourth chapter is about fiber properties of a subanalytic set. Chapter 5 studies subanalytic stratifications and Whitney stratifications. The last part of the book, Chapter 6, on regular points and Nash points, proves the main theorem of this section, namely, the subanalyticity of the set of singular points of a subanalytic set.
The book suits well for graduate students and young researchers.
Reviewer: Viorel Vâjâitu (Bucureşti)
MSC:
| 32B20 | Semi-analytic sets, subanalytic sets, and generalizations |
| 32-02 | Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces |
