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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some theorems on Fredholm maps


Author: A. J. Tromba
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0298713-0
Article copyright: © Copyright 1972 American Mathematical Society