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

DOI:
https://doi.org/10.1090/S0002-9939-96-03352-7

MathSciNet review:
1327024

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Abstract | References | Similar Articles | Additional Information

Abstract: If is continuous and locally injective, then is in fact surjective and a homeomorphism, provided 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:
https://doi.org/10.1090/S0002-9939-96-03352-7

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