$1$-$1$ holomorphic function on a simple closed contour is $1$-$1$ inside the contour?
up vote
1
down vote
favorite
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 at 2:32
0706
387110
add a comment |
up vote
1
down vote
favorite
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 at 2:32
0706
387110
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
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 at 2:32
0706
387110
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 at 2:32
0706
387110
asked Nov 22 at 2:32
0706
387110
edited Nov 22 at 13:21
asked Nov 22 at 2:32
0706
387110
asked Nov 22 at 2:32
0706
387110
asked Nov 22 at 2:32
0706
387110
387110
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3008671%2f1-1-holomorphic-function-on-a-simple-closed-contour-is-1-1-inside-the-co%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
