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Gamboa, J. M.
(1984)
*A note on hyperplane sections of real algebraic sets.*
Boletín de la Sociedad Matemática Mexicana, 29
(2).
pp. 59-63.
ISSN 1405-213X

## Abstract

The author studies the size of the set of hyperplanes which meet a non- zero-dimensional algebraic set V over a real-closed ground field R. More precisely, let us denote by $V\sb c$ the locus of central points of V, i.e., the closure, in the order topology of $R\sp n$, of the set of regular points of V. The author proves the following: There exists a linear isomorphism $\sigma$ of $R\sp n$ such that for every ``generic'' hyperplane H of $R\sp n$, either H meets $V\sb c$ or its transform by $\sigma$ meets $V\sb c$.

Item Type: | Article |
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Uncontrolled Keywords: | Real ground fields |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 17223 |

Deposited On: | 27 Nov 2012 09:43 |

Last Modified: | 01 Mar 2016 17:25 |

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