×

zbMATH — the first resource for mathematics

Some remarks about proper real algebraic maps. (English) Zbl 0964.14046
This paper presents two properness criteria for real polynomial and analytic maps: a real (multivariate) polynomial represents a proper function if all fibers are compact, a real analytic map \({\mathbb R}^n\to{\mathbb R}^m\) is proper if its image is closed and all fibers are compact. The authors also show that any \(C^\infty\) map from \({\mathbb R}^n\) to \({\mathbb R}^m\) can be approximated in the \(C^\infty\) topology by proper polynomial maps.
MSC:
14P05 Real algebraic sets
14R15 Jacobian problem
14E05 Rational and birational maps
PDF BibTeX XML Cite
Full Text: EuDML