(untitled) (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.