Andradas Heranz, CarlosGamboa Mutuberria, José Manuel2023-06-212023-06-2119840030-8730https://hdl.handle.net/20.500.14352/64608We 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 Rn + k. We apply this result to show that any clopen subset of the space of orders of the field of rational functions K= R(X1,...iXn) is the image of the space of orders of a finite extension of K.engjournal articlehttp://projecteuclid.org/pjmopen access512.7Real algebraic varietiesRegularly closed semialgebraic setClopen subsetSpace of orders of rational functionsGeometria algebraica1201.01 Geometría Algebraica