Geometry of Subanalytic and Semialgebraic Sets: Progress in Mathematics, cartea 150

"The main interest of the book is that it contains very deep results, some of which are new even for subanalytic or semialgebraic sets... These results are very important and provide foundations for the development of a 'tame topology' and a 'tame singularity theory.' Shiota's book is indispensable to every mathematician interested in these topics."
-Bulletin of the AMS

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.