Is an open subset of an open set of a topological space open?
$begingroup$
If $X$ is an topological space and $ U subseteq V subseteq X$ with $V$ open in $X$ and $U$ open in $V$, is it true that $U$ is open in $X$?
general-topology
edited Dec 5 '18 at 16:57
Andrews
3901317
asked Dec 5 '18 at 16:07
gengen
4532521
$endgroup$
add a comment |
$begingroup$
If $X$ is an topological space and $ U subseteq V subseteq X$ with $V$ open in $X$ and $U$ open in $V$, is it true that $U$ is open in $X$?
general-topology
edited Dec 5 '18 at 16:57
Andrews
3901317
asked Dec 5 '18 at 16:07
gengen
4532521
$endgroup$
add a comment |
$begingroup$
If $X$ is an topological space and $ U subseteq V subseteq X$ with $V$ open in $X$ and $U$ open in $V$, is it true that $U$ is open in $X$?
general-topology
edited Dec 5 '18 at 16:57
Andrews
3901317
asked Dec 5 '18 at 16:07
gengen
4532521
$endgroup$
If $X$ is an topological space and $ U subseteq V subseteq X$ with $V$ open in $X$ and $U$ open in $V$, is it true that $U$ is open in $X$?
general-topology
general-topology
edited Dec 5 '18 at 16:57
Andrews
3901317
asked Dec 5 '18 at 16:07
gengen
4532521
edited Dec 5 '18 at 16:57
Andrews
3901317
asked Dec 5 '18 at 16:07
gengen
4532521
edited Dec 5 '18 at 16:57
Andrews
3901317
edited Dec 5 '18 at 16:57
Andrews
3901317
edited Dec 5 '18 at 16:57
Andrews
3901317
3901317
asked Dec 5 '18 at 16:07
gengen
4532521
asked Dec 5 '18 at 16:07
gengen
4532521
asked Dec 5 '18 at 16:07
gengen
4532521
4532521
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Yes. $U$ open in $V$ means that $U=Vcap W$ for some $W$ open in $X$. So $U$ is an intersection of two open sets in $X$.
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
$endgroup$
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
add a comment |
$begingroup$
Hint: $U $ is open in $V $ iff $U=Vcap S $ for some $S $ open in $X $.
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
$endgroup$
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
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
});
}
});
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%2f3027254%2fis-an-open-subset-of-an-open-set-of-a-topological-space-open%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes. $U$ open in $V$ means that $U=Vcap W$ for some $W$ open in $X$. So $U$ is an intersection of two open sets in $X$.
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
$endgroup$
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
add a comment |
$begingroup$
Yes. $U$ open in $V$ means that $U=Vcap W$ for some $W$ open in $X$. So $U$ is an intersection of two open sets in $X$.
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
$endgroup$
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
add a comment |
$begingroup$
Yes. $U$ open in $V$ means that $U=Vcap W$ for some $W$ open in $X$. So $U$ is an intersection of two open sets in $X$.
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
$endgroup$
Yes. $U$ open in $V$ means that $U=Vcap W$ for some $W$ open in $X$. So $U$ is an intersection of two open sets in $X$.
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
answered Dec 5 '18 at 16:10
ajotatxeajotatxe
53.8k23890
53.8k23890
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
add a comment |
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
$begingroup$
Thank you (five more characters)
$endgroup$
– gen
Dec 5 '18 at 16:11
add a comment |
$begingroup$
Hint: $U $ is open in $V $ iff $U=Vcap S $ for some $S $ open in $X $.
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
$endgroup$
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
add a comment |
$begingroup$
Hint: $U $ is open in $V $ iff $U=Vcap S $ for some $S $ open in $X $.
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
$endgroup$
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
add a comment |
$begingroup$
Hint: $U $ is open in $V $ iff $U=Vcap S $ for some $S $ open in $X $.
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
$endgroup$
Hint: $U $ is open in $V $ iff $U=Vcap S $ for some $S $ open in $X $.
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
edited Dec 5 '18 at 16:23
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
answered Dec 5 '18 at 16:12
Thomas ShelbyThomas Shelby
2,710421
2,710421
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
add a comment |
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Is this just the definition of U being open in V?
$endgroup$
– gen
Dec 5 '18 at 16:13
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
$begingroup$
Yes. This is how a subspace topology is defined.
$endgroup$
– Thomas Shelby
Dec 5 '18 at 16:15
add a comment |
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%2f3027254%2fis-an-open-subset-of-an-open-set-of-a-topological-space-open%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
