What are the limit points of $X times mathbbN$?order topology and discrete topologySubspace topology and order topologySubspace topology and order topology (2)Convexity implies the equivalence of order and subspace topologiesOrder topology and subspace topology in $mathbb R$What are the limit points of $A_n=[n,infty)$ in a metric space? Is $A_n$ closed?questions about subspace topology, order topology and convex subsetIs the interval $((a,b), (a,d))$ is open in $mathbbRtimes mathbbR$ which is equipped with the dictionary order topologyMunkres Example 16.3Help me to visualise limit points of $S$.
How does a predictive coding aid in lossless compression?
What's the in-universe reasoning behind sorcerers needing material components?
Im going to France and my passport expires June 19th
Can a virus destroy the BIOS of a modern computer?
Intersection Puzzle
Why can't we play rap on piano?
What is the most common color to indicate the input-field is disabled?
Why didn't Boeing produce its own regional jet?
How to prevent "they're falling in love" trope
How can saying a song's name be a copyright violation?
Can I run a new neutral wire to repair a broken circuit?
Little known, relatively unlikely, but scientifically plausible, apocalyptic (or near apocalyptic) events
What does “the session was packed” mean in this context?
A category-like structure without composition?
How to Recreate this in LaTeX? (Unsure What the Notation is Called)
What killed these X2 caps?
Watching something be piped to a file live with tail
Do scales need to be in alphabetical order?
iPad being using in wall mount battery swollen
Arrow those variables!
How much of data wrangling is a data scientist's job?
Cursor Replacement for Newbies
Why didn't Miles's spider sense work before?
One verb to replace 'be a member of' a club
What are the limit points of $X times mathbbN$?
order topology and discrete topologySubspace topology and order topologySubspace topology and order topology (2)Convexity implies the equivalence of order and subspace topologiesOrder topology and subspace topology in $mathbb R$What are the limit points of $A_n=[n,infty)$ in a metric space? Is $A_n$ closed?questions about subspace topology, order topology and convex subsetIs the interval $((a,b), (a,d))$ is open in $mathbbRtimes mathbbR$ which is equipped with the dictionary order topologyMunkres Example 16.3Help me to visualise limit points of $S$.
$begingroup$
Let $X=0,1,2 $ with natural order topology and give $mathbbN$ its natural order topology. Consider $X times mathbbN$ with the dictionary order topology.
What are the limit points of $X times mathbbN$ ?
Answer:
$X times mathbbN=(0,1), (0,2), cdots, (0, infty), (1,1),(1,2), cdots, (1, infty), (2,1), (2,2), cdots, (2, infty) , cdots $
But how to find the limit point?
help me
limits order-topology
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
$endgroup$
|
show 2 more comments
$begingroup$
Let $X=0,1,2 $ with natural order topology and give $mathbbN$ its natural order topology. Consider $X times mathbbN$ with the dictionary order topology.
What are the limit points of $X times mathbbN$ ?
Answer:
$X times mathbbN=(0,1), (0,2), cdots, (0, infty), (1,1),(1,2), cdots, (1, infty), (2,1), (2,2), cdots, (2, infty) , cdots $
But how to find the limit point?
help me
limits order-topology
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
$endgroup$
$begingroup$
Have you tried working with ordinals? Because that would immediately answer this question.
$endgroup$
– Don Thousand
Mar 21 at 7:13
$begingroup$
@DonThousand, Any finite set has all its limits points. But this est $X times mathbbN$ is discrete set, so it is closed and hence all limits points. Is it?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:42
$begingroup$
I wouldn't be so sure about that. Consider $(3,1)$. Any neighborhood around $(3,1)$ must contain an element of the form $(2,n)$ for some $ninmathbb N$. So, $(3,1)$ is a limit point of $Xtimesmathbb N$. Again, thinking about this in terms of ordinals makes this problem a lot easier IMO.
$endgroup$
– Don Thousand
Mar 21 at 7:55
$begingroup$
@DonThousand, what are the open sets look like in $ X times mathbbN$?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:59
$begingroup$
Order topology...google is your best friend.
$endgroup$
– Don Thousand
Mar 21 at 7:59
|
show 2 more comments
$begingroup$
Let $X=0,1,2 $ with natural order topology and give $mathbbN$ its natural order topology. Consider $X times mathbbN$ with the dictionary order topology.
What are the limit points of $X times mathbbN$ ?
Answer:
$X times mathbbN=(0,1), (0,2), cdots, (0, infty), (1,1),(1,2), cdots, (1, infty), (2,1), (2,2), cdots, (2, infty) , cdots $
But how to find the limit point?
help me
limits order-topology
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
$endgroup$
Let $X=0,1,2 $ with natural order topology and give $mathbbN$ its natural order topology. Consider $X times mathbbN$ with the dictionary order topology.
What are the limit points of $X times mathbbN$ ?
Answer:
$X times mathbbN=(0,1), (0,2), cdots, (0, infty), (1,1),(1,2), cdots, (1, infty), (2,1), (2,2), cdots, (2, infty) , cdots $
But how to find the limit point?
help me
limits order-topology
limits order-topology
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
asked Mar 21 at 7:01
M. A. SARKARM. A. SARKAR
2,4621820
2,4621820
$begingroup$
Have you tried working with ordinals? Because that would immediately answer this question.
$endgroup$
– Don Thousand
Mar 21 at 7:13
$begingroup$
@DonThousand, Any finite set has all its limits points. But this est $X times mathbbN$ is discrete set, so it is closed and hence all limits points. Is it?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:42
$begingroup$
I wouldn't be so sure about that. Consider $(3,1)$. Any neighborhood around $(3,1)$ must contain an element of the form $(2,n)$ for some $ninmathbb N$. So, $(3,1)$ is a limit point of $Xtimesmathbb N$. Again, thinking about this in terms of ordinals makes this problem a lot easier IMO.
$endgroup$
– Don Thousand
Mar 21 at 7:55
$begingroup$
@DonThousand, what are the open sets look like in $ X times mathbbN$?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:59
$begingroup$
Order topology...google is your best friend.
$endgroup$
– Don Thousand
Mar 21 at 7:59
|
show 2 more comments
$begingroup$
Have you tried working with ordinals? Because that would immediately answer this question.
$endgroup$
– Don Thousand
Mar 21 at 7:13
$begingroup$
@DonThousand, Any finite set has all its limits points. But this est $X times mathbbN$ is discrete set, so it is closed and hence all limits points. Is it?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:42
$begingroup$
I wouldn't be so sure about that. Consider $(3,1)$. Any neighborhood around $(3,1)$ must contain an element of the form $(2,n)$ for some $ninmathbb N$. So, $(3,1)$ is a limit point of $Xtimesmathbb N$. Again, thinking about this in terms of ordinals makes this problem a lot easier IMO.
$endgroup$
– Don Thousand
Mar 21 at 7:55
$begingroup$
@DonThousand, what are the open sets look like in $ X times mathbbN$?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:59
$begingroup$
Order topology...google is your best friend.
$endgroup$
– Don Thousand
Mar 21 at 7:59
$begingroup$
Have you tried working with ordinals? Because that would immediately answer this question.
$endgroup$
– Don Thousand
Mar 21 at 7:13
$begingroup$
Have you tried working with ordinals? Because that would immediately answer this question.
$endgroup$
– Don Thousand
Mar 21 at 7:13
$begingroup$
@DonThousand, Any finite set has all its limits points. But this est $X times mathbbN$ is discrete set, so it is closed and hence all limits points. Is it?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:42
$begingroup$
@DonThousand, Any finite set has all its limits points. But this est $X times mathbbN$ is discrete set, so it is closed and hence all limits points. Is it?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:42
$begingroup$
I wouldn't be so sure about that. Consider $(3,1)$. Any neighborhood around $(3,1)$ must contain an element of the form $(2,n)$ for some $ninmathbb N$. So, $(3,1)$ is a limit point of $Xtimesmathbb N$. Again, thinking about this in terms of ordinals makes this problem a lot easier IMO.
$endgroup$
– Don Thousand
Mar 21 at 7:55
$begingroup$
I wouldn't be so sure about that. Consider $(3,1)$. Any neighborhood around $(3,1)$ must contain an element of the form $(2,n)$ for some $ninmathbb N$. So, $(3,1)$ is a limit point of $Xtimesmathbb N$. Again, thinking about this in terms of ordinals makes this problem a lot easier IMO.
$endgroup$
– Don Thousand
Mar 21 at 7:55
$begingroup$
@DonThousand, what are the open sets look like in $ X times mathbbN$?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:59
$begingroup$
@DonThousand, what are the open sets look like in $ X times mathbbN$?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:59
$begingroup$
Order topology...google is your best friend.
$endgroup$
– Don Thousand
Mar 21 at 7:59
$begingroup$
Order topology...google is your best friend.
$endgroup$
– Don Thousand
Mar 21 at 7:59
|
show 2 more comments
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%2f3156460%2fwhat-are-the-limit-points-of-x-times-mathbbn%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%2f3156460%2fwhat-are-the-limit-points-of-x-times-mathbbn%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
$begingroup$
Have you tried working with ordinals? Because that would immediately answer this question.
$endgroup$
– Don Thousand
Mar 21 at 7:13
$begingroup$
@DonThousand, Any finite set has all its limits points. But this est $X times mathbbN$ is discrete set, so it is closed and hence all limits points. Is it?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:42
$begingroup$
I wouldn't be so sure about that. Consider $(3,1)$. Any neighborhood around $(3,1)$ must contain an element of the form $(2,n)$ for some $ninmathbb N$. So, $(3,1)$ is a limit point of $Xtimesmathbb N$. Again, thinking about this in terms of ordinals makes this problem a lot easier IMO.
$endgroup$
– Don Thousand
Mar 21 at 7:55
$begingroup$
@DonThousand, what are the open sets look like in $ X times mathbbN$?
$endgroup$
– M. A. SARKAR
Mar 21 at 7:59
$begingroup$
Order topology...google is your best friend.
$endgroup$
– Don Thousand
Mar 21 at 7:59