Piecewise Semialgebraic Sets (Journal of Computational Mathematics, 2005)
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 $C^{μ}$ piecewise semialgebraic sets are also discussed.
Keywords: Algebraic geometry; Semialgebraic geometry; Tarski-Seidenberg Principle; Multivariate splines; Piecewise semialgebraic sets.