Mixing
$1$-$1$ holomorphic function on a simple closed contour is $1$-$1$ inside the contour?
Suppose that $f(z)$ is holomorphic inside and on a simple closed contour $C.$
I'd like to prove the following:
If $f(z)$ is a one-to-one function on $C$, then $f(z)$ is one-to-one function inside $C.$
I don't know how to prove it. The only thing I know is that $f(C)$ is a simple closed contour, since $f$ is one-to-one on a simple closed contour $C$.
Please let me know if you have any idea or comment for this question.
Thanks in advance!
complex-analysis
asked Nov 22 '18 at 2:32
07060706
414110
add a comment |
Suppose that $f(z)$ is holomorphic inside and on a simple closed contour $C.$
I'd like to prove the following:
If $f(z)$ is a one-to-one function on $C$, then $f(z)$ is one-to-one function inside $C.$
I don't know how to prove it. The only thing I know is that $f(C)$ is a simple closed contour, since $f$ is one-to-one on a simple closed contour $C$.
Please let me know if you have any idea or comment for this question.
Thanks in advance!
complex-analysis
asked Nov 22 '18 at 2:32
07060706
414110
add a comment |
Suppose that $f(z)$ is holomorphic inside and on a simple closed contour $C.$
I'd like to prove the following:
If $f(z)$ is a one-to-one function on $C$, then $f(z)$ is one-to-one function inside $C.$
I don't know how to prove it. The only thing I know is that $f(C)$ is a simple closed contour, since $f$ is one-to-one on a simple closed contour $C$.
Please let me know if you have any idea or comment for this question.
Thanks in advance!
complex-analysis
asked Nov 22 '18 at 2:32
07060706
414110
Suppose that $f(z)$ is holomorphic inside and on a simple closed contour $C.$
I'd like to prove the following:
If $f(z)$ is a one-to-one function on $C$, then $f(z)$ is one-to-one function inside $C.$
I don't know how to prove it. The only thing I know is that $f(C)$ is a simple closed contour, since $f$ is one-to-one on a simple closed contour $C$.
Please let me know if you have any idea or comment for this question.
Thanks in advance!
complex-analysis
complex-analysis
asked Nov 22 '18 at 2:32
07060706
414110
asked Nov 22 '18 at 2:32
07060706
414110
edited Nov 22 '18 at 13:21
0706
asked Nov 22 '18 at 2:32
07060706
414110
asked Nov 22 '18 at 2:32
07060706
414110
asked Nov 22 '18 at 2:32
07060706
414110
414110
add a comment |
add a comment |
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