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...

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Detalhes bibliográficos
Autores: Andradas Heranz, Carlos, Gamboa Mutuberria, José Manuel
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
Descrição
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.