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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Weierstrass approximation theorem
and a characterization of the unit circle

Authors: J. Bochnak and W. Kucharz
Journal: Proc. Amer. Math. Soc. 127 (1999), 1571-1574
MSC (1991): Primary 14G30, 14C99
Published electronically: February 17, 1999
MathSciNet review: 1653417
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Abstract: We study real algebraic morphisms from nonsingular real algebraic varieties $X$ with $\dim X \geq 1$ into nonsingular real algebraic curves $C$. We show, among other things, that the set of real algebraic morphisms from $X$ into $C$ is never dense in the space of all $\mathcal C^\infty$ maps from $X$ into $C$, unless $C$ is biregularly isomorphic to a Zariski open subset of the unit circle.

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Additional Information

J. Bochnak
Affiliation: Department of Mathematics, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

W. Kucharz
Affiliation: Department of Mathematics, University of New Mexico, Albuquerque, New Mexico 87131

Received by editor(s): July 29, 1996
Published electronically: February 17, 1999
Additional Notes: Both authors were partially supported by NATO Collaborative Research Grants Programme CRG 960011
The second author was partially supported by NSF Grant DMS-9503138
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society