More on basic semialgebraic sets

Abstract

As is well known, if S is open the 9;'S in this expression can be omitted. Recall also that an open semialgebraic set is called basic open if furthermore p = 1. These basic open sets have attracted a lot of interest in recent times, see :Br2,3!, [Sch], [Mh], [AnBrRzl], culminating in the beautiful theorem that a basic open set S always has a description of the form S = {x EX: JI(x) > 0, ...,fs(x) > O}