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On the complements of 3-dimensional convex polyhedra as polynomial images of ℝ³

Departamento de Álgebra, Facultad de CC. Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

and

Departamento de Matemáticas, IES La Vega de San José, Paseo de San José, s/n, Las Palmas de Gran Canaria, 35015 Las Palmas, Spain

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https://doi.org/10.1142/S0129167X14500712Cited by:7 (Source: Crossref)

Abstract

Let be a convex polyhedron of dimension n. Denote and let be its closure. We prove that for n = 3 the semialgebraic sets and are polynomial images of ℝ³. The former techniques cannot be extended in general to represent the semialgebraic sets and as polynomial images of ℝⁿ if n ≥ 4.

Dedicated to Julio Castellanos on the occasion of his 60th birthday

Keywords:

AMSC: 14P10, 52B10, 52B55, 90C26

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