RT Journal Article
T1 On complements of convex polyhedra as polynomial and regular images of $\R^n$
A1 Fernando Galván, José Francisco
A1 Ueno, Carlos
AB In this work we prove constructively that the complement $\R^n\setminus\pol$ of a convex polyhedron $\pol\subset\R^n$ and the complement $\R^n\setminus\Int(\pol)$ of its interior are regular images of $\R^n$. If $\pol$ is moreover bounded, we can assure that $\R^n\setminus\pol$ and $\R^n\setminus\Int(\pol)$ are also polynomial images of $\R^n$. The construction of such regular and polynomial maps is done by double induction on the number of \em facets \em (faces of maximal dimension) and the dimension of $\pol$; the careful placing (\em first \em and \em second trimming positions\em) of the involved convex polyhedra which appear in each inductive step has interest by its own and it is the crucial part of our technique.
PB Oxford University Press
SN 1073-7928
YR 2014
FD 2014
LK https://hdl.handle.net/20.500.14352/33886
UL https://hdl.handle.net/20.500.14352/33886
LA eng
NO Spanish GR MTM2011-22435,
DS Docta Complutense
RD 18 abr 2025