Semialgebraic set

Summary

A semialgebraic set is a subset of $\R^n$ described by finitely many polynomial equations and strict inequalities combined with "and", "or" and "not". By the Tarski–Seidenberg theorem, the projection of a semialgebraic set is again semialgebraic. Semialgebraic sets have finitely many connected components and admit triangulations. They are the natural objects of real algebraic geometry and the model example of an o-minimal structure.