Piecewise Semialgebraic Sets

Abstract

Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of $R^n$ satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of $C^{\mu}$ piecewise semialgebraic sets are also discussed.