Mixing
Topological space formed by the identification of a unit square
$begingroup$
I know that the first identification "rolls up" the unit square to form a cylinder with open ends but I'm unsure on how the next two "close up" the ends. Does it become a cylinder or more of a cone ending? Also I'm really bad at triangulating surfaces so any help with that would be very useful.
general-topology surfaces triangulation
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
$endgroup$
add a comment |
$begingroup$
I know that the first identification "rolls up" the unit square to form a cylinder with open ends but I'm unsure on how the next two "close up" the ends. Does it become a cylinder or more of a cone ending? Also I'm really bad at triangulating surfaces so any help with that would be very useful.
general-topology surfaces triangulation
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
$endgroup$
$begingroup$
On each circle of the cylinder, the antipodal points get identified, or equivalently you rotate by 180 degrees. This identification doesn't happen nicely in 3-dimensional space.
$endgroup$
– Ben
Jan 30 at 14:21
$begingroup$
Linked.
$endgroup$
– Alex Ravsky
Feb 2 at 14:58
add a comment |
$begingroup$
I know that the first identification "rolls up" the unit square to form a cylinder with open ends but I'm unsure on how the next two "close up" the ends. Does it become a cylinder or more of a cone ending? Also I'm really bad at triangulating surfaces so any help with that would be very useful.
general-topology surfaces triangulation
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
$endgroup$
I know that the first identification "rolls up" the unit square to form a cylinder with open ends but I'm unsure on how the next two "close up" the ends. Does it become a cylinder or more of a cone ending? Also I'm really bad at triangulating surfaces so any help with that would be very useful.
general-topology surfaces triangulation
general-topology surfaces triangulation
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
edited Feb 21 at 14:23
Myles Mckay
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
asked Jan 30 at 10:45
Myles MckayMyles Mckay
1048
1048
$begingroup$
On each circle of the cylinder, the antipodal points get identified, or equivalently you rotate by 180 degrees. This identification doesn't happen nicely in 3-dimensional space.
$endgroup$
– Ben
Jan 30 at 14:21
$begingroup$
Linked.
$endgroup$
– Alex Ravsky
Feb 2 at 14:58
add a comment |
$begingroup$
On each circle of the cylinder, the antipodal points get identified, or equivalently you rotate by 180 degrees. This identification doesn't happen nicely in 3-dimensional space.
$endgroup$
– Ben
Jan 30 at 14:21
$begingroup$
Linked.
$endgroup$
– Alex Ravsky
Feb 2 at 14:58
$begingroup$
On each circle of the cylinder, the antipodal points get identified, or equivalently you rotate by 180 degrees. This identification doesn't happen nicely in 3-dimensional space.
$endgroup$
– Ben
Jan 30 at 14:21
$begingroup$
On each circle of the cylinder, the antipodal points get identified, or equivalently you rotate by 180 degrees. This identification doesn't happen nicely in 3-dimensional space.
$endgroup$
– Ben
Jan 30 at 14:21
$begingroup$
Linked.
$endgroup$
– Alex Ravsky
Feb 2 at 14:58
$begingroup$
Linked.
$endgroup$
– Alex Ravsky
Feb 2 at 14:58
add a comment |
0
active
oldest
votes
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
});
}
});
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%2f3093368%2ftopological-space-formed-by-the-identification-of-a-unit-square%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
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.
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%2f3093368%2ftopological-space-formed-by-the-identification-of-a-unit-square%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
$begingroup$
On each circle of the cylinder, the antipodal points get identified, or equivalently you rotate by 180 degrees. This identification doesn't happen nicely in 3-dimensional space.
$endgroup$
– Ben
Jan 30 at 14:21
$begingroup$
Linked.
$endgroup$
– Alex Ravsky
Feb 2 at 14:58