Mathematics - 2012-08-13 (page 6 of 6)

MeAndMath

9:00 PM

@PeterTamaroff if adds something...

Peter Tamaroff

@MeAndMath Well, it is a nice experience I suppose. It really depends on what use you give it.

skullpatrol

hi @MichaelGreinecker

Michael Greinecker

hi @skullpatrol

MeAndMath

@PeterTamaroff in what sense is it a good experience?talk with a high level mathematician?

Peter Tamaroff

@MeAndMath It depends on you, really. You might love it or you might fall asleep. As I said, wait for it.

MeAndMath

9:03 PM

@PeterTamaroff I`M ANXIOUS ,PETER!

Peter Tamaroff

@t.b. Sorry tb, but I don't see why $\overline {f_\alpha(F)}\subset X_\alpha \setminus V_\alpha$ (I'm wrinting $X_\alpha \setminus V_\alpha$ for you $V^c$)

@MeAndMath I really don't know what to tell you. I guess you will enjoy it.

MeAndMath

@PeterTamaroff I hope so.(if you told me what kind of math stuff did he talked...)

Peter Tamaroff

@MeAndMath Well, about math in general, and about the mathematics of the flight of bats.

t.b.

@PeterTamaroff I chose $V \subset X_\alpha$ in such a way that $f_{\alpha}^{-1}(V) \subset F^{c}$ so that $f_\alpha(F) \subset X_\alpha \smallsetminus V$, which is closed, so $\overline{f_{\alpha}(F)} \subset X_\alpha \smallsetminus V$, too.

Peter Tamaroff

But that doesn't mean he'll talk about that.

MeAndMath

9:08 PM

@PeterTamaroff yes,that´s true.it´s kind a lecture?

t.b.

@JacobSchlather Yes, it's handy, but unfortunately you still need the book nearby because Google books doesn't let you look at the references... :/ but this site is certainly what you should check first in order to find out whether some statement needs some choice.

Kannappan Sampath

bye.

skullpatrol

later

Peter Tamaroff

Oh, yes yes, $$\eqalign{
& f_\alpha ^{ - 1}\left( {{O_\alpha }} \right) \subset X\backslash F \cr
& X\backslash f_\alpha ^{ - 1}\left( {{O_\alpha }} \right) \supset F \cr
& f_\alpha ^{ - 1}\left( {{X_\alpha }\backslash {O_\alpha }} \right) \supset F \cr
& {X_\alpha }\backslash {O_\alpha } \supset {f_\alpha }\left( F \right) \cr} $$

I should think about my set theory a little more!

t.b.

:)

Peter Tamaroff

9:11 PM

@MeAndMath No, no, it is a "talk".

MeAndMath

@PeterTamaroff well,I shall see.It´s this friday.

Peter Tamaroff

@MeAndMath Use ' for apostrophes, not ´

I have it in the question mark "?" key.

t.b.

@PeterTamaroff says the guy who constantly writes "¿" :)

MeAndMath

@PeterTamaroff AH!thanks!

Chris Eagle

When of course ⸘ is correct

Peter Tamaroff

9:14 PM

@t.b. Oh, are they used in your language?

@t.b. ¿What do you even mean? =)

t.b.

@PeterTamaroff No, as far as I know it's a purely Spanish idiosyncrasy :) But you often write the "wrong" question mark sign... A friend of mine encloses his proofs by contradiction by "¿ ... ?"

¿assume that ... then ... a contradiction?

skullpatrol

Is that correct usage in Spanish?

Peter Tamaroff

@t.b. Yes, that because they are one nexto to each other, so I hit the wrong key. Hehe, that's odd.

t.b.

@skullpatrol It has little to do with Spanish up to the Spanish question mark. In Spanish you just enclose your questions with those symbols. E.g. ¿How are you doing?

skullpatrol

@t.b. Thanks, that's what I meant :-)

Old John

9:20 PM

my keyboard has the unfortunate knack of switching to arabic if I accidentally hit shift+CapsLock - very annoying

t.b.

Yeah I saw you perform some "cartoon swearing" (although those tend to use Chinese) :)

user19161

Geezis. Debian 7 is switching to XFCE as the default DE! The world is ending!

Chris Eagle

I had something similar once. Solved it by explicitly deleting all other keyboard layouts from the OS's list

so the shift-to-next-layout hotkey failed

user19161

@skull Nice avatar! I hope nobody complains this time.

Old John

@JasperLoy I actually like XFCE

skullpatrol

9:22 PM

@JasperLoy Thanks ;-D

user19161

@OldJohn I only ever used GNOME seriously. Tried LXDE once, KDE a few times but never XFCE. Maybe I should have a look.

user19161

@skullpatrol Who complained the last time?

t.b.

okay, my time's up for today. See you all soon

user19161

@t.b. See you!

skullpatrol

later

Old John

9:23 PM

@JasperLoy I used it a lot when I had Slackware - they ditched Gnome for KDE, which I really hated

@t.b. night!

user19161

@OldJohn Is the XFCE video player good?

Old John

@JasperLoy not sure - I don't have XFCE at the moment - and don't watch videos :)

user19161

@OldJohn Anyway nowadays distros mix and match applications, so KDE might even have the GNOME player and so on.

Old John

but I suspect there are several video players which will run with XFCE

@JasperLoy yep

skullpatrol

@JasperLoy I think the person who complained last time about my avatar was lactose intolerant :-D

user19161

9:28 PM

Yeah, but one will have to install a lot of libraries. A huge download.

Old John

@JasperLoy that is the drawback

user19161

@skullpatrol I tolerate all things in this world as long as they do not cause others suffering. Unfortunately many people in the world do not think like that, implementing laws which cause others suffering.

skullpatrol

True.

Michael Greinecker

@skullpatrol When was the last time?

skullpatrol

A few months ago I got a week suspension, but it was good for me and I learned a lot.

user19161

9:32 PM

@MichaelGreinecker Long ago. IIRC, the avatar he used was pretty harmless. No nudity shown.

Michael Greinecker

@skullpatrol If it was on may 16, I flagged it.

user19161

@MichaelGreinecker Were you also the one who flagged me that day?

Michael Greinecker

@JasperLoy No.

skullpatrol

@MichaelGreinecker Thanks.

Michael Greinecker

Have I killed the party?

user19161

9:41 PM

@MichaelGreinecker No, don't worry about it.

Fortuon Paendrag

@MichaelGreinecker What are your mathematical interests, Michael?

Michael Greinecker

@Fortuon: My actual research field is game theory. What I enjoy here is measure theory and foundations.

Fortuon Paendrag

@Michael Excellent. We are comrades in measure theory! You are not often in this room, are you?

I would have seen you, otherwise- given the amount of time I spend here.

Michael Greinecker

@Fortuon: I'm sometimes. I was just very busy finishing my thesis. It might also be a time zone thing, I'm in Vienna, Austria.

skullpatrol

@MichaelGreinecker What area of game theory do you specialize in?

Michael Greinecker

9:47 PM

@skullpatrol Non-cooperative, dynamic game theory. And from a "classical" point of view. I Like my players ultrarational.

David Wheeler

o.o building skynet, are you?

skullpatrol

@MichaelGreinecker I hope I didn't offend you too much with my avatar :-)

Michael Greinecker

@skullpatrol I wasn't that offended and didn't think it would lead to a suspension. But I do think it gives a very unprofessional image of M.SE.

skullpatrol

@MichaelGreinecker I agree :-D

user19161

@skullpatrol I would say a suspension is too much.

David Wheeler

9:54 PM

oh dear...what was the avatar in question a picture of?

skullpatrol

@DavidWheeler Cleavage ;-)

user19161

I really care shit about image.

Henry T. Horton

@JasperLoy Then why are you always begging for my pics?

Old John

@JasperLoy that is my excuse for the way I look :)

skullpatrol

LOL

user19161

9:57 PM

@HenryT.Horton Er...

user19161

@OldJohn Seriously, I think you look quite good, beard or no.

David Wheeler

oh. yeah. explicit depiction of prurient images is bad. unlike say, a picture of an atomic bomb, which is just mass murder. that's cool.

Old John

Ah - but you have probably only seen photos when I have tidied myself up a bit :)
Mostly I look like a hobo

user19161

If SE really wanted to be so "professional", might as well do away with avatars altogether.

Michael Greinecker

@David Who has an a-bomb as avatar?

David Wheeler

10:00 PM

lol, are you always this dead serious?

skullpatrol

@DavidWheeler The heat alone from an atomic bomb can turn a football field of sand into glass...

user19161

And I thought mathematicians have a great sense of humour.

Michael Greinecker

It sounded like you were pointing out some double standard here.

I'm an economist, I have no humour.

David Wheeler

i have seen avatars of atomic bombs...but not recently.

user19161

@OldJohn I really love Jonas's current hairdo though!

David Wheeler

10:02 PM

although i think "double standard" isn't quite an apt description. what i mean is: our society is more or less blase about violence, but insists sex is in some sense shameful.

Old John

@JasperLoy It's great, isn't it :

user19161

@DavidWheeler I have never failed to be amazed by the stupidity and evil of mankind.

2

Michael Greinecker

This was blocked as an avatar: gravatar.com/avatar/…

Old John

@MichaelGreinecker WTF??

David Wheeler

it is quite possible to be thought of as "quite moral" by simultaneously decrying excessive nudity, and also "supporting soldiers" (whose main function is to kill other people). says something about sad about our species i think.

2

Old John

10:04 PM

@JasperLoy absolutely - the more I learn about people, the more I like my dog

(not actually true - I don't have a dog!)

David Wheeler

@MichaelGreinecker that image you just linked to, may have been deemed as "too political"

user19161

@OldJohn Yeah, I have been the victim of many evil deeds in my life...

Michael Greinecker

@OldJohn The SE-meta thread is here: meta.stackoverflow.com/questions/28020/moderating-user-avatar

user19161

@OldJohn I think many people in this room have pets.

Michael Greinecker

Btw: I have no intention to ban nuditiy from the internet and am not exactly conservative.

skullpatrol

10:06 PM

@DavidWheeler Two things are infinite: the universe and human stupidity; and I'm not sure about the universe!

David Wheeler

it doesn't matter to me personally if you do or not...your moral standards are not important to me. and i am not trying to imply that you think/feel/do or have felt/thought/done anything wrong

i just find it curious (and always have) that an activity necessary for human survival even acquired negative social connotations

Old John

@DavidWheeler yep - imagine a society that decried that eating and breathing were in some way shameful

user19161

@skullpatrol Was that from Einstein?

Michael Greinecker

I'm not sure that glam-cleavage shock do much to naturalize sexuality. It's the overfucked-but-undersexed thing.

2

David Wheeler

the site says (somewhere) that gravatars are to be PG...i assume the site is privately owned, and they may make whatever rules of usage they wish

skullpatrol

10:09 PM

@JasperLoy Yep.

MeAndMath

@HenryT.Horton Hi ,Henry!

Henry T. Horton

Holas... How did you find me

David Wheeler

@MichaelGreinecker yeah...it's the whole "peek-a-boo" thing....something "forbidden" is behind that curtain

MeAndMath

@HenryT.Horton Just look there...in the right ,below "Mathematics"...

mixedmath

good evening all

skullpatrol

10:13 PM

hi

Michael Greinecker

good evening

MeAndMath

Hello!

skullpatrol

@mixedmath We were just chatting about my suspension over the "cleavage" avatar.

David Wheeler

@MichaelGreinecker i really don't mean to sound as if i'm picking on you...sort of in a weird mood, and chat typing doesn't include "tone of voice"

mixedmath

you were suspended for a "cleavage" avatar?

skullpatrol

10:15 PM

Yep

Michael Greinecker

@David No prob.

mixedmath

@skullpatrol oh - who knew? When did that happen?

Michael Greinecker

@mixedmath may 16

skullpatrol

Did you mark it on your calender :-D

LOL

Michael Greinecker

@skullpatrol It shows up at my list of helpful flags at my profile. no need to remember it

mixedmath

10:18 PM

@MichaelGreinecker Ah - you were the one that flagged him?

that's a funny circle

Michael Greinecker

@mixedmath yes.

skullpatrol

A Vienna circle :-D

user19161

A circular circle.

mixedmath

Here's something that I'm mulling over right now: in this question, which is now closed, one user happened to give two very short answers

and then a different user edited one of his answers to "Answer blanked in preparation for deletion" and added that to the other answer

does that strike you as strange?

user19161

@mixedmath And who approved it?

mixedmath

10:22 PM

oh, the editing was done by a 6k user, so there was no need of approval

but that doesn't make it right, of course

user19161

@mixedmath I have been thinking about the use of multiple answers as well. I guess it does not really matter whether we have one or many.

user19161

Perhaps he belongs to the camp that strictly believes in single answers.

mixedmath

when I saw this, I happened to think of a few times when a certain user who I'll call MK answered twice, and people suggested that he combine them.

But they didn't combine them for him.

there's this unofficial line, where a user doesn't edit an answer for content, but instead for formatting or readability

user19161

@mixedmath Everyone knows who MK is by now.

mixedmath

yes, well, so it goes

user19161

10:25 PM

Even on ELU there is not really a decided formatting style because there is just too much variation.

Michael Greinecker

@mixedmath Maybe you should leave a comment to the 6K user suggesting that editing content is against the community norm.

mixedmath

I was thinking about doing that, especially if it is, in fact, against the community norm

or perhaps I'd raise something on meta

skullpatrol

Do we even have a Norm in the community?

mixedmath

there's tentaclenorm

one mustn't forget tentacles

Michael Greinecker

There are threads on what the appropriate scope of editing is here and here. This seems out of this scope.

Peter Tamaroff

10:32 PM

FINALLY. I finished writing out the goddamn proof.

user19161

@PeterTamaroff Phew!

user19161

@peter I think you are better off asking others about your exercises. But I can answer you if it is simple enough for me. So don't get mad if I don't respond to your pings.

Jonas Teuwen

Our new website... which still sucks too much to go live! 8-).

Peter Tamaroff

@JasperLoy No problem, J.

@JonasTeuwen Dude.

Dude.

Dude. Really.

user19161

@PeterTamaroff What, three dudes!

Peter Tamaroff

10:34 PM

@JonasTeuwen Looks neat

David Wheeler

@JonasTeuwen. dude. your hair is taller than most buildings.

Jonas Teuwen

@DavidWheeler Thanks man!

Peter Tamaroff

@DavidWheeler HAHHAAHAHHAHAHAHAHAHHAAH

user19161

@JonasTeuwen Wow, you are the most cool looking guy there.

Jonas Teuwen

@JasperLoy Thanks.

Peter Tamaroff

10:35 PM

@JasperLoy This is important. Three "Dudes" is like DEFCON 5

David Wheeler

so you are the webmeister, eh? sounds almost like a real job.

Peter Tamaroff

@JonasTeuwen Jasper, I have a problem here.

Old John

I think my hair is now longer than Jonas's - just mine goes in a different direction

Jonas Teuwen

@OldJohn Hmm... 8-).

user19161

My hair is so short that I look like a recruit.

Old John

10:38 PM

(as I get older gravity takes its toll)

user19161

I should try to take a pic this week.

Peter Tamaroff

@JonasTeuwen Remember we said the weak topology of the $f_\alpha$ is that where $f_\alpha^{-1}(O_\alpha)$ is a subbasis?

David Wheeler

@PeterTamaroff that is the correct definition. another way to say it, is: it is initial with respect to the $f_\alpha$

Peter Tamaroff

@DavidWheeler OK. But now Willard is say this:

user19161

@jonas Did you see my announcement above that Debian is changing default to XFCE?

Jonas Teuwen

10:42 PM

@JasperLoy No.

user19161

@JonasTeuwen This has SHOCKED me!

Old John

@JasperLoy I read it a few days ago - I think their reason was size (fitting everything onto a CD/DVD?)

user19161

@OldJohn Yes, what a weird reason!

Old John

@JasperLoy especially in these days when CDs and DVDs are less vital

Michael Greinecker

@Peter: hanging on the edge of my seat: What is Willard saying?

Peter Tamaroff

10:44 PM

Old John

@MichaelGreinecker I have my copy here ...

Henning Makholm

@JonasTeuwen Um, whut? I click on "about us" and the entire description of what the bleep this is about is a job posting, for an unknown position, with unknown requirements (apart from being a Ph.D. student?), doing unknown things for unknown purposes, for an unknonw renumeration??

Old John

Hmm - is "separating closed sets from points" the same thing as the weak topology?

user19161

@OldJohn Fedora can fit all of them in a CD. Just omit the office suite which can always be installed later for example.

Jonas Teuwen

@HenningMakholm Eh... yep. There was a very old website with very bad SQL. I just hacked something together.

Old John

10:47 PM

@JasperLoy exacttly

David Wheeler

any basis is already a sub-basis

Peter Tamaroff

@DavidWheeler Right. digs a hole

Old John

All this topological talk is making me think of working through Willard again - just for fun

Henning Makholm

@JonasTeuwen Heck, it could be hand-written in vi and served as static text/plain for all I care -- if only it would actually reveal what it is all about. A startup doing ... what?

Peter Tamaroff

@OldJohn Do it for the LULZ.

David Wheeler

10:49 PM

for example: say i want the topology on the real line generated by the open intervals. i don't know a priori, whether or not this is actually a basis, until i start to look at some intersections

Jonas Teuwen

@HenningMakholm Good point. I will fix that. There are about 144 items already. Only board shows the correct pictures yay.

Old John

@PeterTamaroff :)

Jonas Teuwen

I did that page with emacs and wordpress fuqed up my nice tabbing 8-(.

Peter Tamaroff

@DavidWheeler All this separating points from closed sets has to do anything with "convergence"? Remember Mariano said the Tychonoff topology is the natural one we work with when dealing with sequences, and the Tycho topology is the weak topology on $\prod X_\alpha$ induced by the projections.

mixedmath

@MichaelGreinecker I like those two meta bits, and that you have reedited the question.

David Wheeler

10:52 PM

that's just the product topology

Old John

@JonasTeuwen I think one of the biggest mistakes made in the development of computing was the invention of "tab"

Peter Tamaroff

@DavidWheeler yes, i know. that's not my question.

Jonas Teuwen

@OldJohn Why?? :-(.

@OldJohn Four spaces, right?

David Wheeler

which follows from the explicit definition of the product topology (using the collection $\{p_\alpha\}$).

Henning Makholm

Hmm. Clicking around a bit more seems to make it more probable that it's some kind of student/social organization than a startup.

Old John

10:54 PM

@JonasTeuwen it would be nice if everyone agreed - but they don't :(

2, 4, 8 seem to be popular choices

David Wheeler

@Peter..ok, what is your question?

Henning Makholm

@OldJohn It's primarily useful because people don't agree. I like to see code with 2-space indentation steps (because my monitor is not infinite in the horizontal direction) -- most of my coworkers want to have 4 (for reasons that escape me). Set editors to different tab sizes, and everyone is happy.

Old John

@HenningMakholm except when you are writing code which has to handle text full of tabs - and you don't know which size of tab they intended :(

Henning Makholm

@OldJohn They don't belong anywhere but in source code, and source code must never make any difference between kinds or amounts of whitespace anyway.

Old John

@HenningMakholm yes - but I am talking about writing code to handle and display text supplier by "users" and there is no way to control their usage of tabs

Peter Tamaroff

10:59 PM

@DavidWheeler What is the use of the weak topologies? (I know the "simple" ones: subspace topologies (inclusion mapping), quotient topology (identification mapping), and product topology (projections).

Mariano Suárez-Alvarez

@BillDubuque, I have deleted a message from you which I did not read

Jack Schmidt

@OldJohn This requires an EE to implement website controlled electrical shocks on the tab key.

Old John

@HenningMakholm trust me - I spent some years running a website with user-supplied text (from school maths teachers) and at times it was a nightmare

@JackSchmidt Excellent!

Bill Dubuque

@MarianoSuárez-Alvarez Ok, I will flag your comment then. Thanks for your uncooperation.

Mariano Suárez-Alvarez

As I wrote a while ago, I will not read any message from you which is not CCed to all the other mods

Bill Dubuque

11:02 PM

@MarianoSuárez-Alvarez Do as you wish...

Mariano Suárez-Alvarez

I usually do

David Wheeler

usually the strong topology is used for the quotient topology, because you are given q (the surjection), rather than an induced map.

but you originally asked about "convergence"

well, i ask you: what is convergence?

Peter Tamaroff

@MarianoSuárez-Alvarez Mariano, remember you said the product topology is the "natural" topology we usually use without thinking about.

Mariano Suárez-Alvarez

yes

Peter Tamaroff

@MarianoSuárez-Alvarez What did you mean?

@DavidWheeler I usually think about it in terms of nbhs.

Mariano Suárez-Alvarez

11:06 PM

an element of a product can be viewed as a function (from the set of indices)

Peter Tamaroff

@MarianoSuárez-Alvarez Yes.

Mariano Suárez-Alvarez

the usual topology of the produc t is that of pointwise convergence

when you view its elements as functions

David Wheeler

the point i'm trying to get at: is that usually we speak of convergence of "sequences"

which is a function $f:\Bbb N \to X$

Peter Tamaroff

@DavidWheeler Right. That is what Mariano is saying.

(I guess =P)

David Wheeler

but this can be generalized to use more general sets than just the natural numbers for the index

the usual choice is a "directed set", a set with a partial order in which every two elements have an upper bound

Mariano Suárez-Alvarez

11:11 PM

that is a detail which can safely be left to a later time :-)

checking that a sequence in a product converges iff it converges pointwise is a sufficiently illuminating exercise!

Peter Tamaroff

@DavidWheeler Like a lattice but without the $\inf$...?

Mariano Suárez-Alvarez

nothing is gained from clobbering one;'s mind with a ton of different things at the same time

Peter Tamaroff

@MarianoSuárez-Alvarez True.

David Wheeler

for example, remember "the arrow" in that book you were looking at?

Peter Tamaroff

@DavidWheeler Yes.

Jonas Teuwen

11:14 PM

Now I need API! API for LinkedIn, Twitter, Facebook! AUTOPOSTING.

Peter Tamaroff

@MarianoSuárez-Alvarez Does it have something to do with the fact a function $f:Y\to \prod_{\alpha \in A}X_\alpha$ is continuous $\iff$ all the $\pi_\alpha f=f_\alpha$ are continuous?

Mariano Suárez-Alvarez

of course it has to do with that

because that is more or less the definition of the product topology

Peter Tamaroff

@MarianoSuárez-Alvarez I supposed.

@MarianoSuárez-Alvarez Yes.

Mariano Suárez-Alvarez

what else could it have to do with? :-)

Peter Tamaroff

@MarianoSuárez-Alvarez Hehehe well...

Old John

11:15 PM

@JonasTeuwen APIs are great - until they change the rules without telling you :)

David Wheeler

the collection of those intervals form a directed set, if we set (a,∞) ≤ (b,∞) when a ≤ b.

Jonas Teuwen

@OldJohn The old webmaster didn't seem to care about security :-/.

Wadaqfuq everything chmod 777.

Old John

@JonasTeuwen ROFL!!

Jonas Teuwen

@OldJohn 8-).

Old John

@JonasTeuwen Select * from webmasters where has-a-clue > 0

Jonas Teuwen

11:20 PM

@OldJohn DROP; 8-).

David Wheeler

one can regard a real sequence (in the sense of first-year calculus) as a point in $\Bbb R^\omega = \prod_{n \in \Bbb N} \Bbb R$ (countable copies of the real numbers)

Jonas Teuwen

Oh > 0...

Old John

I only deal with the ones who have a clue :)

Time I went unconscious for a few hours - later folks

BenjaLim

@DavidWheeler I have posted a new AT question on the main page.

Jonas Teuwen

@OldJohn Bye!

Old John

11:26 PM

@JonasTeuwen Bye

Jonas Teuwen

@OldJohn Bye :-).

BenjaLim

@OldJohn bye

@MarianoSuárez-Alvarez Hey

I posted an answer to one of your questions on MO :D

Mariano Suárez-Alvarez

I saw :-)

BenjaLim

@MarianoSuárez-Alvarez thermonuclear weapon or pea shooter?

@MarianoSuárez-Alvarez I was doing this the other day as an exercise in Munkres

then I recalled that an alternative interpretation of $T(M)$

Mariano Suárez-Alvarez

bazooka

BenjaLim

11:33 PM

@MarianoSuárez-Alvarez how come it's not a tomahawk

@MarianoSuárez-Alvarez I am now trying to build my own backbone for AT

Mariano Suárez-Alvarez

That argumen is actually not quite absurd, really

BenjaLim

@MarianoSuárez-Alvarez how come?

have you seen it before?

David Wheeler

@BenjaLim what is $\alpha$ indexed by?

BenjaLim

@DavidWheeler some index set

not necessarily countable, or whatever

Bill Dubuque

@MarianoSuárez-Alvarez Bezouka!

Mariano Suárez-Alvarez

11:35 PM

My objection, Ben, would be more that it is more of a detour than an awfully sophisticated proof

BenjaLim

@MarianoSuárez-Alvarez :(

@MarianoSuárez-Alvarez I thought it was sophisticated enough

David Wheeler

@BenjaLim i'm not convinced that U is open

BenjaLim

@DavidWheeler I am told by my lecturer it is.

Peter Tamaroff

@MarianoSuárez-Alvarez I once read a proof that $5!$ wasn't odd with some abstract algebra. =P

BenjaLim

@MarianoSuárez-Alvarez Can you help to answer this

Peter Tamaroff

11:38 PM

Using theory about "solvability of permutation groups" or something like that.

No idea what it is though.

David Wheeler

well, the first thing that occurs to me is: what is the dimension of X?

BenjaLim

@PeterTamaroff you need to learn about groups

Peter Tamaroff

@BenjaLim I know what groups are, don't worry.

Tiempo al tiempo.

BenjaLim

@DavidWheeler I don't know.

Not stated at all.

Mariano Suárez-Alvarez

@BenjaLim, show that the set is in fact discrete

BenjaLim

11:39 PM

what is?

Mariano Suárez-Alvarez

indeed, the interior of each cell is an open set in the space

and that gives you disjoint open neighborhoods

BenjaLim

@DavidWheeler Sorry I forgot to add that $A$ was path connected

@MarianoSuárez-Alvarez firstly: What if my $y_\alpha$ is on the boundary of the disk.

Mariano Suárez-Alvarez

and then prove that a discrete set ((in a T_2 space) is closed

well, if they are in the boundary then I do not think the set is closed

BenjaLim

Ok. So I need to be careful in selecting my $y_\alpha$. Fair enough.

2nd question

Peter Tamaroff

@MarianoSuárez-Alvarez Here

BenjaLim

11:41 PM

You claim that two cells that are not different don't overlap? Otherwise why would that give me disjoint open neighbourhoods? @MarianoSuárez-Alvarez

Mariano Suárez-Alvarez

you are only attaching cells on their boundaries

BenjaLim

@MarianoSuárez-Alvarez really?

Mariano Suárez-Alvarez

well, if you are not, then you should

the attaching maps are defined on the boundary of the cells

BenjaLim

oh sorry. What I meant is, it is clear that if you attach one cell to $A$ then it is attached along the boundary.

Call now Y the space $A \cup e$

$e$ is the cell attached.

How do I know if I attach another cell $e'$ to $Y$

that $e'$ won't overlap with $e$?

@MarianoSuárez-Alvarez It's details like these that are not spelt out in Hatcher..

Mariano Suárez-Alvarez

well, if this is an abrirary attachement, then no

CW-complexes, usually, are built in steps

attaching all n-cells at the same time

BenjaLim

11:45 PM

hmmmmmmmm

Mariano Suárez-Alvarez

so in that case the interiores are disjoint

BenjaLim

@MarianoSuárez-Alvarez hah, I never knew about this.

I always thought they were all slapped on at the same time

Mariano Suárez-Alvarez

one can check that, up to homotopy equivalence, this does not matter

BenjaLim

and besides in hatcher it's as if because $\alpha$ is arbitrary

David Wheeler

well...wait a minute, even if you get a continuous curve made up of the $y_\alpha$, won't leaving out the "tube" formed by the curve be open in Y?

BenjaLim

11:47 PM

dunno

David Wheeler

or put another way: a line is closed in $\Bbb R^3$, for example. heck, even a plane is.

Mariano Suárez-Alvarez

if you take a point out of every cell you attach you do get the same original space, up to homotopy, by the way, if the space is a CW complex

do it with one cell

in any case, Hatcher is not the best place to learn the technicaliies of CW-complexes, IMO

try a book like Switzer's or Whitehead's

user19161

@MarianoSuárez-Alvarez Do you think one should learn simplicial complexes first or CW-complexes?

Mariano Suárez-Alvarez

@PeterTamaroff cr.yp.to/talks/2003.03.23/slides.pdf

I would suggest doing both at the same time, mostly

simplicial complexes are regular cw-complexes

David Wheeler

aren't you taking a class with Hatcher as the text, @BenjaLim?

user19161

11:57 PM

@DavidWheeler A text he really hates.

Mariano Suárez-Alvarez

most spaces can be waaaay more efficiently described as cw-complexes, but it is easy to go from the cw-complex to an homeomorphic simplicial complex

BenjaLim

@MarianoSuárez-Alvarez So you say I should do it with attaching one $3$ - cell first?

Mariano Suárez-Alvarez

yes

ALWAYS do that

BenjaLim

In that case I think it should be easy enough.

David Wheeler

well, if the class he's in is using that text, he's kinda stuck with working with it

Mariano Suárez-Alvarez

11:58 PM

consider the simplest possible sitation

BenjaLim

@MarianoSuárez-Alvarez In that case my first question is answered.

Mariano Suárez-Alvarez

@DavidWheeler, I doubt he will be failed for looking elsewhere

he is asking me...

Peter Tamaroff

@MarianoSuárez-Alvarez Hahahahaha I just scanned through it, but WOW.

BenjaLim

@MarianoSuárez-Alvarez ?

Mariano Suárez-Alvarez

Switzer and WHitehead are rather advanced books

but their treatment of cw-complexes is excellent

and comprehensible

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$Mathematics$ Mathematics