A note on projections of real algebraic varieties.
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 Rn + k. We apply this result to show that any clopen s...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 1984 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64608 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/64608 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.7 Real algebraic varieties Regularly closed semialgebraic set Clopen subset Space of orders of rational functions Geometria algebraica 1201.01 Geometría Algebraica |
| Resumo: | 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 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. |
|---|