## Nonlinear Fredholm maps of index zero and their singularities

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- by R. A. Plastock
- Proc. Amer. Math. Soc.
**68**(1978), 317-322 - DOI: https://doi.org/10.1090/S0002-9939-1978-0464283-2
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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 $B = \{ x|F’(x)$ 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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## Bibliographic Information

- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**68**(1978), 317-322 - MSC: Primary 58B15; Secondary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0464283-2
- MathSciNet review: 0464283