Locally injective maps in Ominimal structures without poles are surjective
Author:
Adam H. Lewenberg
Journal:
Proc. Amer. Math. Soc. 124 (1996), 28392844
MSC (1991):
Primary 03C60, 06F20; Secondary 26B99, 54C30
MathSciNet review:
1327024
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Abstract: If is continuous and locally injective, then is in fact surjective and a homeomorphism, provided is definable in an ominimal expansion without poles of the ordered additive group of real numbers; `without poles' means that every onevariable definable function is locally bounded. Some general properties of definable maps in ominimal 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 UrbanaChampaign, Urbana, Illinois 61801
Email:
adams@math.uiuc.edu
DOI:
http://dx.doi.org/10.1090/S0002993996033527
PII:
S 00029939(96)033527
Keywords:
Piecewise linear topology,
PLtopology,
ominimal theory,
ominimal 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
