Mathematics - 2015-07-15 (page 1 of 3)

robjohn

12:07 AM

@Cristopher Are you familiar with the fact that $|\sin(x)|\le|x|$?

Cristopher

@robjohn No, this is the first time I've read it. Would that be another way to prove the limit?

Karl Kronenfeld

@Christopher One (easily corrected) error is that $\arcsin(\varepsilon)$ may simply not exist.

Cristopher

@Karl How can it be corrected?

robjohn

@Cristopher If $\varepsilon\gt1$ use $\delta=\frac\pi2$

Karl Kronenfeld

Anyway, using robjohn's idea makes for a less cumbersome proof.

Cristopher

12:19 AM

@robjohn Okay. Could you tell me how the proof would be if we use $|\sin(x)|\leq|x|$? I don't see it very well yet...

Clarinetist

Is anyone here familiar with branching processes?

@Cristopher Choose $\delta = \epsilon$. Then $|\sin(x)| \leq |x| < \epsilon$.

Cristopher

@Clarinetist Really? Is it that simple? faceplam haha...

Clarinetist

@Cristopher Analysis can be frustrating sometimes :)

Cristopher

Thanks, @Clarinetist. And yes, I know. I'm struggling with these proofs... :)

Thank you @robjohn :)

Stan Shunpike

1:15 AM

@TedShifrin Hey Ted! I've found some stuff to answer that last problem, but I have to figure it out. Some guy explained a bit of it too me, but his answer involved the IFT. math.stackexchange.com/a/1354690/197705

morphic

1:33 AM

Hi @TedShifrin

Ted Shifrin

Hi again, mr eyeglasses

@Stan: I think that's pretty much the proof I gave in the book. I didn't look carefully. Yes, it uses the Implicit F Thm.

morphic

@TedShifrin Did you find a new house already?

mixedmath

1:54 AM

I guesstimate that in 80 days, MSE will have 100000 unanswered questions

Ted Shifrin

Renting in San Diego, yes, mr eyeglasses ...

I thought most of the stupid questions got answered, @mixedmath.

mixedmath

@TedShifrin unfortunately, most the of stupid questions that do get answered have answers that don't get upvoted

well, most isn't true. But very often

Ted Shifrin

Stupid question answers usually get way more votes than the answers that take me an hour ...

morphic

@TedShifrin Someone from UCSD came to a logic conference at our school last week

mixedmath

@TedShifrin yes, I know that feeling

Stan Shunpike

2:02 AM

@TedShifrin hows moving going?

Ted Shifrin

@Stan: The movers come to pack and load Friday/Saturday. I'll be very glad to get through the next month. Getting cable/internet started at the new place is turning out to be a challenge, too ...

Stan Shunpike

Cable is soooo expensive!

Ted Shifrin

I have no association whatsoever with UCSD, @morphic.

Well, @Stan, living is expensive, too.

Stan Shunpike

LOL true. But I thought you said you were renting, don't they have to have like cables and stuff already hooked up to the building?

How hard can it be after that?

morphic

In my experience those were only included in rent when I had roommates

Ted Shifrin

2:07 AM

Well, getting my landlord to call them up to cancel his service is a prerequisite to their making new arrangements with me, @Stan ... :( He'll get around to it eventually.

Stan Shunpike

Uggghhh

morphic

...

Ted Shifrin

Anyhow, @Stan, yes, one needs the implicit function theorem ... and then it's some nice linear algebra about perps (or annihilators, if you know those).

Fargle

Evening, chat.

morphic

Hi @Fargle

Stan Shunpike

2:10 AM

Brb

Ted Shifrin

heya @Fargle ... how you doin' ?

Fargle

Alright. I'd like to have gone out tonight, but I guess I can try to be productive meanwhile. And you, @Ted?

Ted Shifrin

Were you going out anywhere fun?

I'm happy to be unproductive ... down to the last days of organizing for the move.

Fargle

Well, no. I was trying to make plans and they never coalesced. It'd be as simple as hanging out at a friend's house, though. Strange as it may seem (heh), I'm not much for parties.

And that's good to hear.

Ted Shifrin

I didn't quite expect you to be a party animal :) That's not the average behavior of serious math students :)

Fargle

2:16 AM

"Serious" is a strong word.

Ted Shifrin

I consider you as such.

Fargle

I'm flattered. :3

Ted Shifrin

Even if you have abandoned differential geometry ... sob sob :D

Fargle

I haven't abandoned it! I'm just...stalling?

morphic

I think I will take diff geo. in 2016

Ted Shifrin

2:19 AM

I'll try to be around to see that, mr eyeglasses.

user2815185

2:37 AM

why are there so many people in here while stats is empty?

Fargle

Pure math is cool and stats isn't. ;)

(NOT REALLY!)

flakmonkey

anyone have any idea how to approach this question?

user2815185

stats rocks

Stan Shunpike

@TedShifrin whats your favorite branch of math?

user2815185

Stats is kind of like math

just more... dynamic

morphic

2:40 AM

Mathematical culinary

Paco_Da_Taco

stats is like Math with uncertainty

Eric Stucky

You could sell it as a self-help tool if you called it "quantum math".

morphic

Quantum culinary

Paco_Da_Taco

oooh, I like the sound of that. Henceforth statistics will be known as quantum math

schrodinger's math

Mike Miller

@flakmonkey: There's a standard way of expressing the unit disc as a union of squares. (Draw the biggest square you can; now one on top, to the left, to the right, underneath; etc...) Figure out how much area you're gaining in each step. This formula should help you figure out how close the size of your dyadic squares need to be to the original size of the squares to get within $\varpesilon$ of the whole area with finitely many.

flakmonkey

2:44 AM

@MikeMiller thank you!

Is the proof that there is a way of expressing the unit disc as a union of squares simple?

Mike Miller

Actually, the above is too complicated. Just tile the whole plane with squares of a given dyadic area, and show that by decreasing the radius they take up more and more of the area of the unit disc. (Bound the area of the union of the squares that intersect the unit disc above; show that as the area of the squares decreases, this goes to zero.)

morphic

What does "dyadic square/area" mean

Mike Miller

Dyadic rational is a rational of the form $a/2^n$, $a$ an integer.

anon

the unit disc is the union of all the squares it contains

okay, you want finitely many dyadic ones with total area arbitrarily close

flakmonkey

3:03 AM

@anon why is the unit disc the union of all the squares it contains?

anon

because every point in the disk is inside a square that is inside the disc

Mike Miller

3:16 AM

@anon: we want them to intersect only along the boundary

Masacroso

3:27 AM

a quick and I think easy question guys, how can you justify formally than $\lim_{x \to + \infty} 1^x=1$?

Fargle

@Masacroso Pick $\epsilon > 0$; note that we may choose any $M \in \Bbb R$, and it will be the case that if $x > M$, $|1^x - 1| = 0 < \epsilon$, and we are done.

Masacroso

ty very much @Fargle

Fargle

No problem.

user147690

5:35 AM

A module is just a vector space over a ring, rather than a vector space over a field?

user147690

Meaning the scalars form a ring rather than a field, is what I mean to say, i.e. we may not have inverses for our scalars

Samuel Yusim

yeah

however aside from the operations behaving how you'd want, very little carries over to a general $R$-module from linear algebra, in my experience

user147690

That seems a valid concern

Samuel Yusim

e.g., considering $\mathbb{Z}/2\mathbb{Z}$ as a $\mathbb{Z}$-module, the set $\{1\}$ is linearly dependent because of the nontrivial linear combination $2 \cdot 1 = 0$

user147690

Oh jeez xD

Samuel Yusim

5:40 AM

because of this, there's no well-defined notion of dimension or anything like it in the general case

user147690

Interesting

Samuel Yusim

you can look up free modules for the next best thing though

I'd say more but I need to go to bed

user147690

That's fine, thanks for the example

user147690

I have just started the chapter in Artin

Alec Teal

o/

Balarka Sen

5:49 AM

@AlexClark yes, that is correct. a modules is an abelian group with an R-action. a vector space is an abelian group with an F-action. this makes the notion of vector spaces a special case of modules.

Alec Teal

@AlexClark you've been quiet.

Balarka Sen

as @SamuelYusim hinted, classifying modules is hard, unlike vector spaces.

user147690

@AlecTeal Non-math distracted me for a little over a week, and after that I have been working on the research project for tropical geometry

user147690

@BalarkaSen That (R/F)-action is scalar multiplication from the linear algebra perspective?

Balarka Sen

Right.

Alec Teal

5:53 AM

Well I've noticed no changes since your exams, nor replies (Worm diagrams Alex, WORM DIAGRAMS!)

user147690

Eric Stucky

This was an odd time to come back to chat.

user147690

Ahahaha

user147690

My diagram above was a joke admittedly

user147690

@AlecTeal How do I read this worm diagram?

Alec Teal

5:57 AM

Top down

It should be pretty obvious

user147690

It isn't

Alec Teal

Link it

user147690

I looked up worm diagram, but my picture above shows my dilemma

Alec Teal

Okay, well each coloured bar is the state of a book.

Red indicates read lots, and blue not read. Grey skimmed, as usual.

user147690

6:00 AM

Wait so, each bar going down vertically is at a different time?

user147690

I.e. each time you update it?

Alec Teal

Yeah.

user147690

Okay that was the integral piece of information (that I was missing) lol

user147690

That's really awesome

Alec Teal

Yeah, I can see how knowing about kisogo.com, the domain of that image and stuff would make it a hard concept to grasp :P

To see your "diagrams" login and they'll appear on book pages. to make them public go to a volume, then volume control, then add public link

user147690

6:02 AM

I kind of wish you always had this feature :P

Alec Teal

I told you before, the data was there. I wrote it during exam season it was only really meant to store and display

Anyway, the data is live. Despite the ".png" access rule. (That's just mod-rewrite)

Stan Shunpike

@AlecTeal I feel like this could be used in psych research

Alec Teal

I feel like I'm the only one using it.

Stan Shunpike

I dont know. But graphs and how you represent data matter. And this is a nifty way to spot patterns

Alec Teal

I also wrote a mediawiki plugin that can display like your most recently read 5 things and such (also live)

user147690

6:05 AM

@AlecTeal Well it doesn't help that I fell behind and I have so much to update into it

Alec Teal

I'm working on auto-linking sources (opt in of course)

Balarka Sen

@AlexClark I like Atiyah-MacDonald's list of examples of A-modules : 1) A = k; k-vector space 2) A = Z; abelian group (any abelian group is a Z-module by defining the Z-action as $n \cdot x = x + \cdots + x$ (n times). any Z-module is an abelian group by forgetting about the Z-action structure). 3) A = k[x]; an A-module with a linear transformation (the linear transformation M --> M is obtained from restricting the action A x M --> M to (x, -), i.e., the x-action)

4) A = k[G]; k-representations of G (an A-action on M inducesa hom A --> End(M). this gives you a hom G --> End(M))

Alec Teal

No but what little data there is is still graphable Alex

Balarka Sen

the side-notes inside the parenthesis are there for an explanation, btw.

Alec Teal

user147690

6:08 AM

@BalarkaSen Thanks for the list, I will go get that book now aswell

Balarka Sen

No, don't.

user147690

Don't?

user147690

I remember someone recommending it for algebraic geometry anyway?

Alec Teal

Oh @AlexClark I also added inline theorem boxes (see maths.kisogo.com/index.php?title=Subspace_topology for example)

Balarka Sen

It's not meant for beginners. It talks very little, for one.

Learn about modules thoroughly from somewhere else first.

user147690

6:09 AM

@AlecTeal It would be nice if I could edit the read fields in the volume information page(kisogo.com/book/volume.php?VolumeId=64)

user147690

@BalarkaSen Alright, modules->commutative algebra->algebraic geometry?

Balarka Sen

e.g., I have added the explanations in the parenthesis. A-M just gives a list of things, and lets you figure out if it's right or not. He does that to almost everything :P

@AlexClark sure, if you want. that'd take some fair amount of time, though!

what kind of algebraic geometry d'you want to learn?

user147690

@BalarkaSen Well I wanted to learn toric varieties - but that led me to find many algebraic geometry words and concepts I don't know

Alec Teal

@AlexClark I can't see that page

user147690

@AlecTeal I just mean on the volumeID pages

Alec Teal

6:11 AM

There is a button to make adding them a bit faster. There's an entirely re-written version almost done (that'll require no DB changes!) and is MUCH much nicer.

user147690

When will you release that?

Alec Teal

It also supports exam papers and stuff, and there's an API (that goes both ways) so for example, I can link maths.kisogo.com solution pages right to the volumes

Hopefully on Friday

Balarka Sen

@AlexClark I don't know what it is either. Seems like you have to hunt through Grothendieck-type algebraic geometry.

user147690

I will hold off on updating until then, since I have 20 textbooks with pages scattered all over them

Alec Teal

It'll then run live at beta.kisogo.com (same DB) then be switched over on Monday is all goes well.

user147690

6:13 AM

@BalarkaSen Well question: What is a non-topological torus?

Balarka Sen

I don't know.

user147690

Well that's what toric varieties are based upon it seems

Balarka Sen

Where did you find that terminology?

Alec Teal

@AlexClark you should do that now. The beta will be in "read only" mode until the transition.

user147690

One sec

Balarka Sen

6:14 AM

Right, I just google, and it turned up algebraic torus.

The definition seems involved. You have to learn much more than classic algebraic geometry to grok that, it seems.

Alec Teal

@AlexClark use it by Friday. I shall not ask again

user147690

@AlecTeal That's a little full on

user147690

I have to go now, need to pack up(at uni atm)

Alec Teal

@AlexClark I'm fed up now, so that really was an ultimatum

user147690

I don't like ultimatums

Alec Teal

6:19 AM

Oh noes

@AlexClark you're also... not using mathjax? Seriously? codecogs.com/latex/usage.php

Martin Sleziak

@AlecTeal What kind of wiki is that. Is there some general information about that website?

3

Is it your personal wiki?

Alec Teal

6:44 AM

@MartinSleziak I own/host/wrote-most of it but it isn't "mine" personally. It will however be ad-free forever and stuff, I can guarantee you that.

Alec Teal

7:03 AM

Night then. Before I go @MartinSleziak I wont e annoying and link pages you'll never read but there's a lot of good stuff there. I actually use it A LOT. It's really handy to link in answers as it has the definitions (always, at the top, first thing) but then see also and immediate properties and such.

Anyway, night

Later pal.

@BalarkaSen hi

hello

what is the attaching word of the 2-cell in this space?

(1 sec)

i.e. take $D^2$, remove two open disks and identify all boundary circles

Balarka Sen

recall that this space is a punctured torus with a cylinder attached to the bd of the puncture and one of the longitudes.

so instead, you can give it a two 2-cell CW structure, which is seemingly simpler than doing it with one 1-cell.

the words are simpler in this case too. try this one out!

iwriteonbananas

7:14 AM

ok

so there's no way to immediatly see the attaching word otherwise?

Balarka Sen

i don't know. the one 2-cell structure freaks me out a bit.

iwriteonbananas

me too

Martin Sleziak

Thanks for the reply, Alec Teal!

iwriteonbananas

@BalarkaSen im looking for the most algorithmic solution in case i don't immediately recognise the homotopy type in the exam

but i think this particular problem would be too hard for my exam anyway

we didnt do much cellular homology

Balarka Sen

there is no algorithmic way for finding cell complex structure of a given space.

use cellular only if your space has an easy cell structure.

iwriteonbananas

7:23 AM

ok

Balarka Sen

in this case, you're given an identification space. the best you could do is to try doing the identifications by hand and see where it leads you

mayer-vietoris is easiest in this case, as we've discussed previously

iwriteonbananas

fair enough

a couple days ago i asked you about finding all 2-sheeted coverings of $S^1\vee S^1$

Balarka Sen

i have pinged you about that one in the alg top chat

El'endia Starman

7:49 AM

3

An animation of my own making!

Square grid, all movement is strictly along x or y axis, apparent curving is because of hyperbolic geometry.

skill patrol

9:41 AM

@El'endiaStarman nice work :-)

Soham Chowdhury

12:09 PM

hey chat

Soham Chowdhury

12:23 PM

aw, shucks, chat is ded

user2290820

hye guys anyone knows about n-parasitic numbers and how to find it in bases other than 10? its got me overthinking about it

robjohn

@SohamChowdhury long live chat!

user2290820

continuing from above, I thought of applying same logic as base10 here:

$$2 * num_{base} = lastdigit * base^{digitlen - 1} + firstnum$$
ref post here: https://math.stackexchange.com/questions/1361368/n-parasitic-number-in-a-base-different-than-10

but that doesn't work

skill patrol

@SohamChowdhury viva las chat!

user147690

@AlecTeal Yeah, using a plugin since the other plugin needed me to download a bunch of files and I just wanted to get it done

user147690

12:37 PM

@AlecTeal I see you are using simplemathjax, and I am just using simplemath - what are the advantages?

user147690

@BalarkaSen What more than algebraic geometry?

user147690

Fairly sure it was this that I found it @Balarka gen.lib.rus.ec/…

user147690

I found it to read more about polyhedral fans/cones

Balarka Sen

12:56 PM

@AlexClark I said much more than classic algebraic geometry.

Schemes aren't classical algebraic geometry.

user147690

1:43 PM

@BalarkaSen Apologies, that makes sense

Balarka Sen

no need to apologize.

user147690

Hey @SohamChowdhury

Balarka Sen

hey @Soham

Soham Chowdhury

hey. :)

was est up, @Alex?

user147690

nothing much xD. Least math today for ages though, since I went rock climbing

Soham Chowdhury

1:46 PM

I'm studying for a chemistry test. Although it's not what I would call real chemistry -- it's all sorts of numerical crap.

user147690

Ahhh that's not so fun

Soham Chowdhury

@AlexClark ah, cool. getting more and more ripped by the day? :P

Remember me

Hello@SohamChowdhury@AlexC

user147690

Oh god haha, it didn't go too great, girl I was with did better than me xD

user147690

I am really strong, but I am really heavy now, so I can't endure

user147690

1:47 PM

Hey Sayan

Balarka Sen

rock climbing is useless. everything excluding math is useless.

3

user147690

hahaha

user147690

It was fun :P

Remember me

True!!

user147690

Also not entirely sure if you were joking

Soham Chowdhury

1:48 PM

another star-farming comment from the great B

3

user147690

HAHA

Remember me

Haha

Soham Chowdhury

I have gone rock climbing exactly once. I'm pretty sure that I'll say exactly the same thing if you ask me about it twenty years later. :P

user147690

Wait was he joking or not

Balarka Sen

that is better left ambiguous.

3

this is getting silly.

user147690

1:49 PM

I didn't star that one for what it's worth

Soham Chowdhury

Balarka should do research in numerical methods of farming.

user147690

lmao

Remember me

The star panel is in tatters!! :p

Soham Chowdhury

he seems good at it

user147690

How much alg geometry have you done @BalarkaSen?

Soham Chowdhury

1:50 PM

eek.

that's a Bengali cussword, @Alex

Balarka Sen

none so far.

user147690

Oh really? How long have you been working on comm alg?

user147690

Alg? @SohamChowdhury

user96343

Star-farming? I haven't come across this term before.

Balarka Sen

@AlexClark tried doing it a long time ago, but done alg top instead.

Soham Chowdhury

1:51 PM

@AlexClark no, your other contraction. nevermind, I just thought B might be sensitive or something.

user147690

Ohhh

Soham Chowdhury

you're having fun, @Alex?

with comm alg?

user147690

Oh I haven't started really

Balarka Sen

i have started doing A-M again recently.

Soham Chowdhury

ah, good luck.

molarity calls

user147690

1:52 PM

Alright yes, I will be back in 40 or not until tomorrow aswell

user147690

cya later @Rememberme @SohamChowdhury @BalarkaSen

Remember me

@SohamChowdhury done normality?

Cya

Balarka Sen

bye

skill patrol

later pal

Remember me

@BalarkaSen what's A-M?

Balarka Sen

1:54 PM

a book on commutative algebra. contraction of atiyah-macdonald.

Remember me

Ohh...

@BalarkaSen does there exist any other space except a point ,line ,plane to which there always exists a quotient map from any given structure ?

Balarka Sen

I don't know. I don't think about the quotient map like Munkres does. I think of it as the natural map $X \to X/G$.

Remember me

Hmm...

Balarka Sen

Did you think about normal subgroups anymore afterwards?

Remember me

Yes ... I did and I was trying to find an example of a normal subgroup...

Any abelian subgroup of a group does the job right?

Balarka Sen

2:00 PM

Exactly.

For a nonabelian example, $D_{2n}$ and the subgroup of all rotations.

Remember me

Yes...

Balarka Sen

@Rememberme Careful! Did you mean any subgroup of an abelian group?

"any abelian subgroup of a group is normal" is false.

Example : $D_{2n}$ and the group of all reflections (isomorphic to $\Bbb Z/2$, which is abelian)

Remember me

I meant an abelian subgroup.. A subgroup which is abelian .. Not the group

Balarka Sen

then what you said is false

Remember me

@BalarkaSen

Why?

Balarka Sen

2:10 PM

i just gave you an example above

Remember me

Okay so every subgroup won't be most of 'em will be...

Balarka Sen

no, that too is false

why should it be true?

you have a group $G$ and a subgroup $H$ and an action $g \cdot h = ghg^{-1}$. you want to prove that this is well defined, that is, for every $h \in H$ and $g \in G$, $ghg^{-1}$ is in $H$. what you want is to have the total group $G$ to be abelian, as then $gh = hg$, implying $ghg^{-1} = h \in H$ by left-cancellation.

Remember me

Hmm... I have to go it seems .. I will surely come back to you next when I come back online @BalarkaSen

Balarka Sen

ok, I have to go too.

morphic

Later guys

skill patrol

2:19 PM

later

pals

:-)

Alec Teal

2:40 PM

@AlexClark mathjax looks A LOT better. Because it's vector graphics instead. Also all you do is put something in the extensions folder, it's not a lot of work.

user147690

@AlecTeal What's something in this case? It seemed I needed to download a few things, but it might have been a different extension. Is is still <math></math> based?

Alec Teal

@AlexClark you can also get plugins for mathjax, like say: maths.kisogo.com/index.php?title=Xypic xypic here. Which is great!

@AlexClark that's just the tag, That's arbitrary, as you know I use <m> and <mm> for inline/display math respectively. I left <math> only because stuff already uses it.

maths.kisogo.com/… check out that diagram, isn't that sweet.

user147690

"Alec's 'super' diagram"

user147690

It is indeed sweet xD

Alec Teal

@AlexClark if you zoom in on your one, you'll see the maths gets all fuzzy and not smooth, zoom in on mathjax and you'll find it gets sharper and sharper.

user147690

2:43 PM

Yeah just saw that, although I don't know if anyone will be zooming in

Alec Teal

It makes a big difference on screens made in the last 3 years.

It's VERY noticeable on both my laptops and extremely so on my tablet

user147690

Both of mine were in the last 3 years haha

Alec Teal

And you can't tell?

user147690

I can if I zoom for sure

user147690

Anyway I must sleep now, talk later

morphic

2:45 PM

Bye Alex C.

Alec Teal

.... are your laptops 800x600 or something?

WHAT YEAR IS IT?!

morphic

CRT monitor

Mary Star

3:14 PM

Hello!!

skill patrol

Hi!!

morphic

3:32 PM

Hi @MaryStar and @skullpatrol

skill patrol

Hi pal

morphic

I am ಠ_ಠ

2

user183297

Hi, everybody. Can someone check my final results here: http://math.stackexchange.com/questions/1362135/2-exercises-finding-the-limit-and-showing-continuity-and-differentiability#

Cause people commented but nobody gave me final answer is it correct. I'll be thankful.

2 not hard exercises, with a little work to do, but I wrote the whole calculations, so it shouldnt be hard

Remember me

4:17 PM

Hello eyes @morphic

Semiclassical

morning chat

Zain Patel

http://math.stackexchange.com/questions/1362280/pl4201-power-line-overheating-in-laptop

Can we all just vote to close this already?

morphic

@Semiclassical hi!!

Semiclassical

yeah, that's pretty bad. i've gone and voted to close as off-topic

morphic

"I actually checked there is a site for bicycle repair but none for laptop on Stack Exchange"

lol

Zain Patel

4:27 PM

I'm just shaking my head in amazement. xD

iluso

Greetings
http://math.stackexchange.com/questions/1358792/number-of-unordered-factorizations-into-k-distinct-parts
Does anyone have an idea? Is the question clear? I thought it would get more than 18 view in 2 days

Eric Stucky

4:47 PM

The question is clear

but I don't have an idea :/

Hippalectryon

@iluso :-) refresh the page

morphic

Thank you @Hippalectryon

Very kind of you

iluso

@Hippalectryon Oh thanks!

Btw, this could provide a way to answer this (mine to)
http://math.stackexchange.com/questions/1315109/distributing-groups-of-objects-into-boxes

Hippalectryon

Well once someone put a 500 bounty on one of my questions :P I'm just redistributing that

I'll look at it, I gtg for dinner :-)

morphic

Later @Hippalectryon

Remember me

5:15 PM

Ahh... I get it now @BalarkaSen

I found an example...

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5:49 PM

@Fargle Can I ask you a question ? Its about topology

Fargle

Sure. I may be out of my element, though.

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No problem , I just want your views on it

does there exist any other space except a point ,line ,plane to which there always exists a quotient map from any given structure ?

Fargle

Alrighty.

Hmm. I don't know. That's definitely a question I'm not equipped to answer, haha.

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Hmm..

Thanks , anyways

Eric Stucky

Remember: what do you mean by "any given structure"?

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5:53 PM

@Eric I mean any given space as in the unit sphere,$S^1\times S^1$,etc

Eric Stucky

I don't think this can be true, because a quotient map has to be surjective, and finite topologies exist

Maybe one of the two- or three- point topologies will work, but something is telling me no.

ermmm my brain went

completely off the rails a sec

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I want a full fledged proof @Eric or else I won't be able to make my brain happy

Eric Stucky

What I mean is that of your three examples only "point" can be valid.

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Yes I just found an example where the line doesn't work

Unit sphere@Eric

Eric Stucky

(please stop tagging me I'm right here :/)

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5:57 PM

Okay sorry.

Eric Stucky

So if the theorem is "The point is the only topology $A$ for which there exists a quotient map $X\to A$ for all $T$", then the goal is "Given a topology $A$ with at least two points, construct a topology $X$ for which it is not a quotient."

For that we need some kind of quotient invariant ?

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Can you explain me what you mean by a quotient invariant

Eric Stucky

I mean, like, homotopy is a homeomorphism invariant

Order of a group is an isomorphism invariant

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okay..

Eric Stucky

etc. etc.

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$Mathematics$ Mathematics