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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Locally injective maps in O-minimal
structures without poles are surjective


Author: Adam H. Lewenberg
Journal: Proc. Amer. Math. Soc. 124 (1996), 2839-2844
MSC (1991): Primary 03C60, 06F20; Secondary 26B99, 54C30
MathSciNet review: 1327024
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Abstract: If $f:\mathbf R^m\to \mathbf R^m$ is continuous and locally injective, then $f$ is in fact surjective and a homeomorphism, provided $f$ is definable in an o-minimal expansion without poles of the ordered additive group of real numbers; `without poles' means that every one-variable definable function is locally bounded. Some general properties of definable maps in o-minimal expansions of ordered abelian groups without poles are also established.


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Additional Information

Adam H. Lewenberg
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: adams@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03352-7
PII: S 0002-9939(96)03352-7
Keywords: Piecewise linear topology, PL-topology, o-minimal theory, o-minimal structure, proper map, surjective local homeomorphism
Received by editor(s): May 27, 1994
Received by editor(s) in revised form: March 14, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society