What does it mean to say that a topology is defined by a metric?
up vote
1
down vote
favorite
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
asked Nov 22 at 4:02
伽罗瓦
1,080615
add a comment |
up vote
1
down vote
favorite
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
asked Nov 22 at 4:02
伽罗瓦
1,080615
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 at 4:43
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
asked Nov 22 at 4:02
伽罗瓦
1,080615
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
general-topology
asked Nov 22 at 4:02
伽罗瓦
1,080615
asked Nov 22 at 4:02
伽罗瓦
1,080615
edited Nov 22 at 4:04
asked Nov 22 at 4:02
伽罗瓦
1,080615
asked Nov 22 at 4:02
伽罗瓦
1,080615
asked Nov 22 at 4:02
伽罗瓦
1,080615
1,080615
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 at 4:43
add a comment |
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 at 4:43
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 at 4:03
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 at 4:43
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 at 4:43
add a comment |
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',
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%2f3008726%2fwhat-does-it-mean-to-say-that-a-topology-is-defined-by-a-metric%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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%2f3008726%2fwhat-does-it-mean-to-say-that-a-topology-is-defined-by-a-metric%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
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 at 4:43