How to construct a homeomorphism on closed unit disc onto itself which fixes boundary point wise?
0
$begingroup$
How can we construct a homeomorphism on closed disc onto itself which fixes boundary pointwise? What is the starting point.
general-topology group-theory analysis differential-geometry
asked Jan 8 at 22:52
ershersh
438113
$endgroup$
|
show 1 more comment
0
$begingroup$
How can we construct a homeomorphism on closed disc onto itself which fixes boundary pointwise? What is the starting point.
general-topology group-theory analysis differential-geometry
asked Jan 8 at 22:52
ershersh
438113
$endgroup$
2
$begingroup$
You could use the identity... it fixes the boundary (and all other points).
$endgroup$
– Clayton
Jan 8 at 22:54
$begingroup$
Well that is trivial! I am looking for non-trivial ones.
$endgroup$
– ersh
Jan 8 at 22:56
$begingroup$
How can I write the formula for this transformation?
$endgroup$
– ersh
Jan 8 at 23:02
3
$begingroup$
$f(r,theta)=(r,theta+2pi r)$
$endgroup$
– Lee Mosher
Jan 8 at 23:15
2
$begingroup$
@kesa OP is looking for maps that fix every point on the boundary. The only holomorphic map that does this is the identity.
$endgroup$
– Kavi Rama Murthy
Jan 8 at 23:23
|
show 1 more comment
0
0
0
$begingroup$
How can we construct a homeomorphism on closed disc onto itself which fixes boundary pointwise? What is the starting point.
general-topology group-theory analysis differential-geometry
asked Jan 8 at 22:52
ershersh
438113
$endgroup$
How can we construct a homeomorphism on closed disc onto itself which fixes boundary pointwise? What is the starting point.
general-topology group-theory analysis differential-geometry
general-topology group-theory analysis differential-geometry
asked Jan 8 at 22:52
ershersh
438113
asked Jan 8 at 22:52
ershersh
438113
edited Jan 8 at 22:57
ersh
asked Jan 8 at 22:52
ershersh
438113
asked Jan 8 at 22:52
ershersh
438113
asked Jan 8 at 22:52
ershersh
438113
438113
2
$begingroup$
You could use the identity... it fixes the boundary (and all other points).
$endgroup$
– Clayton
Jan 8 at 22:54
$begingroup$
Well that is trivial! I am looking for non-trivial ones.
$endgroup$
– ersh
Jan 8 at 22:56
$begingroup$
How can I write the formula for this transformation?
$endgroup$
– ersh
Jan 8 at 23:02
3
$begingroup$
$f(r,theta)=(r,theta+2pi r)$
$endgroup$
– Lee Mosher
Jan 8 at 23:15
2
$begingroup$
@kesa OP is looking for maps that fix every point on the boundary. The only holomorphic map that does this is the identity.
$endgroup$
– Kavi Rama Murthy
Jan 8 at 23:23
|
show 1 more comment
2
$begingroup$
You could use the identity... it fixes the boundary (and all other points).
$endgroup$
– Clayton
Jan 8 at 22:54
$begingroup$
Well that is trivial! I am looking for non-trivial ones.
$endgroup$
– ersh
Jan 8 at 22:56
$begingroup$
How can I write the formula for this transformation?
$endgroup$
– ersh
Jan 8 at 23:02
3
$begingroup$
$f(r,theta)=(r,theta+2pi r)$
$endgroup$
– Lee Mosher
Jan 8 at 23:15
2
$begingroup$
@kesa OP is looking for maps that fix every point on the boundary. The only holomorphic map that does this is the identity.
$endgroup$
– Kavi Rama Murthy
Jan 8 at 23:23
2
2
$begingroup$
You could use the identity... it fixes the boundary (and all other points).
$endgroup$
– Clayton
Jan 8 at 22:54
$begingroup$
You could use the identity... it fixes the boundary (and all other points).
$endgroup$
– Clayton
Jan 8 at 22:54
$begingroup$
Well that is trivial! I am looking for non-trivial ones.
$endgroup$
– ersh
Jan 8 at 22:56
$begingroup$
Well that is trivial! I am looking for non-trivial ones.
$endgroup$
– ersh
Jan 8 at 22:56
$begingroup$
How can I write the formula for this transformation?
$endgroup$
– ersh
Jan 8 at 23:02
$begingroup$
How can I write the formula for this transformation?
$endgroup$
– ersh
Jan 8 at 23:02
3
3
$begingroup$
$f(r,theta)=(r,theta+2pi r)$
$endgroup$
– Lee Mosher
Jan 8 at 23:15
$begingroup$
$f(r,theta)=(r,theta+2pi r)$
$endgroup$
– Lee Mosher
Jan 8 at 23:15
2
2
$begingroup$
@kesa OP is looking for maps that fix every point on the boundary. The only holomorphic map that does this is the identity.
$endgroup$
– Kavi Rama Murthy
Jan 8 at 23:23
$begingroup$
@kesa OP is looking for maps that fix every point on the boundary. The only holomorphic map that does this is the identity.
$endgroup$
– Kavi Rama Murthy
Jan 8 at 23:23
|
show 1 more comment
1 Answer
1
active
oldest
votes
5
$begingroup$
u can just do a rotation which tend to zero angle when you go torward the boundary and to some other angle while you are going torward the centre
answered Jan 8 at 23:01
tommycauterotommycautero
888
$endgroup$
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
3
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
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%2f3066833%2fhow-to-construct-a-homeomorphism-on-closed-unit-disc-onto-itself-which-fixes-bou%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
5
$begingroup$
u can just do a rotation which tend to zero angle when you go torward the boundary and to some other angle while you are going torward the centre
answered Jan 8 at 23:01
tommycauterotommycautero
888
$endgroup$
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
3
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
add a comment |
5
$begingroup$
u can just do a rotation which tend to zero angle when you go torward the boundary and to some other angle while you are going torward the centre
answered Jan 8 at 23:01
tommycauterotommycautero
888
$endgroup$
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
3
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
add a comment |
5
5
5
$begingroup$
u can just do a rotation which tend to zero angle when you go torward the boundary and to some other angle while you are going torward the centre
answered Jan 8 at 23:01
tommycauterotommycautero
888
$endgroup$
u can just do a rotation which tend to zero angle when you go torward the boundary and to some other angle while you are going torward the centre
answered Jan 8 at 23:01
tommycauterotommycautero
888
answered Jan 8 at 23:01
tommycauterotommycautero
888
answered Jan 8 at 23:01
tommycauterotommycautero
888
answered Jan 8 at 23:01
tommycauterotommycautero
888
888
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
3
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
add a comment |
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
3
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
$begingroup$
How would I write such a map?
$endgroup$
– ersh
Jan 8 at 23:32
3
3
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
polar coordinates
$endgroup$
– tommycautero
Jan 8 at 23:36
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
$begingroup$
Yes!..let me try.
$endgroup$
– ersh
Jan 8 at 23:37
add a comment |
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3066833%2fhow-to-construct-a-homeomorphism-on-closed-unit-disc-onto-itself-which-fixes-bou%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
2
$begingroup$
You could use the identity... it fixes the boundary (and all other points).
$endgroup$
– Clayton
Jan 8 at 22:54
$begingroup$
Well that is trivial! I am looking for non-trivial ones.
$endgroup$
– ersh
Jan 8 at 22:56
$begingroup$
How can I write the formula for this transformation?
$endgroup$
– ersh
Jan 8 at 23:02
3
$begingroup$
$f(r,theta)=(r,theta+2pi r)$
$endgroup$
– Lee Mosher
Jan 8 at 23:15
2
$begingroup$
@kesa OP is looking for maps that fix every point on the boundary. The only holomorphic map that does this is the identity.
$endgroup$
– Kavi Rama Murthy
Jan 8 at 23:23