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

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. Front Matter....Pages I-IX Introduction....Pages 1-3 A First Look at Semialgebraic Geometry....Pages 5-28 Real Algebra....Pages 29-60 Spaces of Signs....Pages 61-84 Spaces of Orderings....Pages 85-123 The Main Results....Pages 125-143 Spaces of Signs of Rings....Pages 145-176 Real Algebra of Excellent Rings....Pages 177-210 Real Analytic Geometry....Pages 211-253 Back Matter....Pages 255-270