Question on point set topologyDefinition of Borel setsA “complementary” topologyFinite vs infinite distinction in Rudin's AnalysisThe set of rationals in $(0,1)$ is not a $G_delta$Limit point of an infinite subset of a compact setIf $U ⊂ mathbbR^n$ is open and $B ⊂ U$, then why is it that $B$ relatively open in $U$ if and only if $B$ is open?Question about Theorem 2.24 in Baby RudinShowing that if closed subsets don't intersect then there exists open sets in which they exist that also don't intersectDifference between closure and closed cover of a setIs there an analogue for a compact set using closed sets?
Does the attack bonus from a Masterwork weapon stack with the attack bonus from Masterwork ammunition?
Describing a chess game in a novel
What are substitutions for coconut in curry?
How can an organ that provides biological immortality be unable to regenerate?
Synchronized implementation of a bank account in Java
Is there a term for accumulated dirt on the outside of your hands and feet?
Does .bashrc contain syntax errors?
Why is indicated airspeed rather than ground speed used during the takeoff roll?
When did antialiasing start being available?
Do I need to consider instance restrictions when showing a language is in P?
Do I need to be arrogant to get ahead?
Am I eligible for the Eurail Youth pass? I am 27.5 years old
How to terminate ping <dest> &
How are passwords stolen from companies if they only store hashes?
Pronounciation of the combination "st" in spanish accents
Geography in 3D perspective
Deletion of copy-ctor & copy-assignment - public, private or protected?
How does 取材で訪れた integrate into this sentence?
PTIJ: Do Irish Jews have "the luck of the Irish"?
Can a medieval gyroplane be built?
What is the English word for a graduation award?
Brake pads destroying wheels
Is it insecure to send a password in a `curl` command?
A Ri-diddley-iley Riddle
Question on point set topology
Definition of Borel setsA “complementary” topologyFinite vs infinite distinction in Rudin's AnalysisThe set of rationals in $(0,1)$ is not a $G_delta$Limit point of an infinite subset of a compact setIf $U ⊂ mathbbR^n$ is open and $B ⊂ U$, then why is it that $B$ relatively open in $U$ if and only if $B$ is open?Question about Theorem 2.24 in Baby RudinShowing that if closed subsets don't intersect then there exists open sets in which they exist that also don't intersectDifference between closure and closed cover of a setIs there an analogue for a compact set using closed sets?
1
$begingroup$
Does there exist a closed set which is an intersection of a collection of infinite open sets?
analysis
asked 1 hour ago
Tony TongTony Tong
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
1
$begingroup$
Does there exist a closed set which is an intersection of a collection of infinite open sets?
analysis
asked 1 hour ago
Tony TongTony Tong
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
5
$begingroup$
Intersect $(-tfrac1n, tfrac1n)$ for $n = 1, 2, ldots$ and consider what set you get
$endgroup$
– Brevan Ellefsen
1 hour ago
$begingroup$
Oh it will get $0$
$endgroup$
– Tony Tong
58 mins ago
add a comment |
1
1
1
$begingroup$
Does there exist a closed set which is an intersection of a collection of infinite open sets?
analysis
asked 1 hour ago
Tony TongTony Tong
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Does there exist a closed set which is an intersection of a collection of infinite open sets?
analysis
analysis
asked 1 hour ago
Tony TongTony Tong
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Tony TongTony Tong
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Tony TongTony Tong
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Tony TongTony Tong
322
asked 1 hour ago
Tony TongTony Tong
322
322
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Tony Tong is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
5
$begingroup$
Intersect $(-tfrac1n, tfrac1n)$ for $n = 1, 2, ldots$ and consider what set you get
$endgroup$
– Brevan Ellefsen
1 hour ago
$begingroup$
Oh it will get $0$
$endgroup$
– Tony Tong
58 mins ago
add a comment |
5
$begingroup$
Intersect $(-tfrac1n, tfrac1n)$ for $n = 1, 2, ldots$ and consider what set you get
$endgroup$
– Brevan Ellefsen
1 hour ago
$begingroup$
Oh it will get $0$
$endgroup$
– Tony Tong
58 mins ago
5
5
$begingroup$
Intersect $(-tfrac1n, tfrac1n)$ for $n = 1, 2, ldots$ and consider what set you get
$endgroup$
– Brevan Ellefsen
1 hour ago
$begingroup$
Intersect $(-tfrac1n, tfrac1n)$ for $n = 1, 2, ldots$ and consider what set you get
$endgroup$
– Brevan Ellefsen
1 hour ago
$begingroup$
Oh it will get $0$
$endgroup$
– Tony Tong
58 mins ago
$begingroup$
Oh it will get $0$
$endgroup$
– Tony Tong
58 mins ago
add a comment |
1 Answer
1
active
oldest
votes
6
$begingroup$
$$mathbbRcapmathbbRcapmathbbRcapcdots$$
answered 1 hour ago
parsiadparsiad
18.5k32453
$endgroup$
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
1
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
1
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
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
);
);
Tony Tong is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3152433%2fquestion-on-point-set-topology%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
6
$begingroup$
$$mathbbRcapmathbbRcapmathbbRcapcdots$$
answered 1 hour ago
parsiadparsiad
18.5k32453
$endgroup$
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
1
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
1
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
add a comment |
6
$begingroup$
$$mathbbRcapmathbbRcapmathbbRcapcdots$$
answered 1 hour ago
parsiadparsiad
18.5k32453
$endgroup$
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
1
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
1
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
add a comment |
6
6
6
$begingroup$
$$mathbbRcapmathbbRcapmathbbRcapcdots$$
answered 1 hour ago
parsiadparsiad
18.5k32453
$endgroup$
$$mathbbRcapmathbbRcapmathbbRcapcdots$$
answered 1 hour ago
parsiadparsiad
18.5k32453
answered 1 hour ago
parsiadparsiad
18.5k32453
answered 1 hour ago
parsiadparsiad
18.5k32453
answered 1 hour ago
parsiadparsiad
18.5k32453
18.5k32453
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
1
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
1
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
add a comment |
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
1
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
1
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
$begingroup$
But R is an open set, the intersection is also R so it is still an open set
$endgroup$
– Tony Tong
1 hour ago
1
1
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
$begingroup$
And also closed
$endgroup$
– Keen-ameteur
1 hour ago
1
1
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
While extremely simple, this example has the unfortunate side effect of also being open, which could further confound the OP who seems to be wondering why the intersection of open sets is not open in general (admittedly, the OP is probably also drawing a false dichotomy between open and closed sets, so I suppose this helps with that)
$endgroup$
– Brevan Ellefsen
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
$begingroup$
@BrevanEllefsen: +1, but I couldn't resist... :-)
$endgroup$
– parsiad
56 mins ago
add a comment |
Tony Tong is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
Tony Tong is a new contributor. Be nice, and check out our Code of Conduct.
Tony Tong is a new contributor. Be nice, and check out our Code of Conduct.
Tony Tong is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3152433%2fquestion-on-point-set-topology%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
5
$begingroup$
Intersect $(-tfrac1n, tfrac1n)$ for $n = 1, 2, ldots$ and consider what set you get
$endgroup$
– Brevan Ellefsen
1 hour ago
$begingroup$
Oh it will get $0$
$endgroup$
– Tony Tong
58 mins ago