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Some theorems on Fredholm maps
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Let
f
:
M
→
N
f:M \to N
be a
C
1
{C^1}
proper Fredholm map of index
n
of
C
r
{C^r}
Banach manifolds. Then under certain hypotheses one may approximate
f
by a
C
r
{C^r}
proper Fredholm map
g
of index
n
with
g
C
1
{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.
American Mathematical Society (AMS)
Title: Some theorems on Fredholm maps
Description:
Let
f
:
M
→
N
f:M \to N
be a
C
1
{C^1}
proper Fredholm map of index
n
of
C
r
{C^r}
Banach manifolds.
Then under certain hypotheses one may approximate
f
by a
C
r
{C^r}
proper Fredholm map
g
of index
n
with
g
C
1
{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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