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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
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