Locally semialgebraic spaces
The book is intended as a ''topologie générale'' for semi-algebraic geometry over a real closed field. Having developed in several papers the study of semi-algebraic spaces and maps, the authors felt the necessity of introducing more general objects, namely locally semialgebraic spaces. Locally semialgebraic spaces are necessary in order to define, for example, a good theory of semialgebraic coverings: the universal covering of a semialgebraic space is no more semialgebraic but locally semialgebraic. The authors develop in three chapters definitions and results about locally semialgebraic spaces and their topological properties (completions, triangulation, homotopy theory), adapting to their case the techniques of topology.
semi-algebraic geometry over a real closed field
scientific article; zbMATH DE number 3931165