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Fernando Galván, José Francisco and Gamboa, J. M. and Ueno, Carlos
(2011)
*On convex polyhedra as regular images of R(n).*
Proceedings of the London Mathematical Society, 103
.
pp. 847-878.
ISSN 0024-6115

PDF
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Official URL: http://plms.oxfordjournals.org/content/103/5/847.full.pdf+html

URL | URL Type |
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http://www.cambridge.org/ | Publisher |

## Abstract

We show that convex polyhedra in R(n) and their interiors are images of regular maps R(n) -> R(n). As a main ingredient in the proof, given an n-dimensional, bounded, convex polyhedron K subset of R(n) and a point p is an element of R(n) \ K, we construct a semialgebraic partition {A, B, T} of the boundary partial derivative K of K determined by p, and compatible with the interiors of the faces of K, such that A and B are semialgebraically homeomorphic to an (n - 1)-dimensional open ball and J is semialgebraically homeomorphic to an (n - 2)-dimensional sphere. Finally, we also prove that closed balls in R n and their interiors are images of regular maps R(n) -> R(n).

Item Type: | Article |
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Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15062 |

Deposited On: | 03 May 2012 09:16 |

Last Modified: | 09 Aug 2018 07:46 |

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