Some theorems on Fredholm maps
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- by A. J. Tromba PDF
- Proc. Amer. Math. Soc. 34 (1972), 578-585 Request permission
Abstract:
Let $f:M \to N$ be a ${C^1}$ proper Fredholm map of index n of ${C^r}$ Banach manifolds. Then under certain hypotheses one may approximate f by a ${C^r}$ proper Fredholm map g of index n with g ${C^1}$ properly homotopic to f. The rank theorem for Fredholm maps is stated and it is then used to obtain the invariance of domain for this class of maps and also a nonlinear version of the Fredholm alternative theorem.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 578-585
- MSC: Primary 58B15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0298713-0
- MathSciNet review: 0298713