A note on projections of real algebraic varieties
Carlos Andradas Heranz, J. M. Gamboa · Pacific Journal of Mathematics · 1984
We prove that any regularly closed semialgebraic set of R", where R is any real closed field and regularly closed means that it is the closure of its interior, is the projection under a finite map of an irreducible algebraic variety in some R n + k .We apply this result to show that any clopen subset of the space of orders of the field of rational functions K= R(X 1 ,..is the image of the space of orders of a finite extension of K.