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

 

Nonlinear Fredholm maps of index zero and their singularities


Author: R. A. Plastock
Journal: Proc. Amer. Math. Soc. 68 (1978), 317-322
MSC: Primary 58B15; Secondary 47H15
MathSciNet review: 0464283
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Abstract: Let $ F:X \to Y$ be a $ {C^1}$ Fredholm map of index zero between two Banach spaces. Defining the singular set $ B = \{ x\vert F'(x)$ is not surjective}, we study the local and global effect of B on the map F. In particular it is shown that if $ b \in B$ is isolated in B, then, for $ \dim X$ and $ \dim Y \geqslant 3$, F is a local homeomorphism at b. We then show that if B consists of discrete points, F is a global homeomorphism of X onto Y. A nonlinear partial differential equation is included as an illustration.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0464283-2
PII: S 0002-9939(1978)0464283-2
Keywords: Fredholm map of index zero, covering space map, proper
Article copyright: © Copyright 1978 American Mathematical Society