9:00 PM

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

hi @MichaelGreinecker

hi @skullpatrol

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

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

9:03 PM
@PeterTamaroff IM ANXIOUS ,PETER!

@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.

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

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

@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.

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

9:08 PM
@PeterTamaroff yes,that´s true.it´s kind a lecture?

@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.

later

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!

:)

9:11 PM
@MeAndMath No, no, it is a "talk".

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

@MeAndMath Use ' for apostrophes, not ´
I have it in the question mark "?" key.

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

@PeterTamaroff AH!thanks!

When of course ⸘ is correct

9:14 PM
@t.b. Oh, are they used in your language?
@t.b. ¿What do you even mean? =)

@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?

Is that correct usage in Spanish?

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

@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?

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

9:20 PM
my keyboard has the unfortunate knack of switching to arabic if I accidentally hit shift+CapsLock - very annoying

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!

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.

@JasperLoy I actually like XFCE

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?

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

user19161
@t.b. See you!

later

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?

@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.

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

@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.

@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.

True.

@skullpatrol When was the last time?

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.

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

user19161
@MichaelGreinecker Were you also the one who flagged me that day?

@JasperLoy No.

@MichaelGreinecker Thanks.

Have I killed the party?

user19161
9:41 PM
@MichaelGreinecker No, don't worry about it.

@MichaelGreinecker What are your mathematical interests, Michael?

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

@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.

@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.

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

9:47 PM
@skullpatrol Non-cooperative, dynamic game theory. And from a "classical" point of view. I Like my players ultrarational.

o.o building skynet, are you?

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

@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.

@MichaelGreinecker I agree :-D

user19161
@skullpatrol I would say a suspension is too much.

9:54 PM
oh dear...what was the avatar in question a picture of?

@DavidWheeler Cleavage ;-)

user19161
I really care shit about image.

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

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

LOL

user19161
9:57 PM
@HenryT.Horton Er...

user19161
@OldJohn Seriously, I think you look quite good, beard or no.

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.

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.

@David Who has an a-bomb as avatar?

10:00 PM
lol, are you always this dead serious?

@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.

It sounded like you were pointing out some double standard here.
I'm an economist, I have no humour.

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

user19161
@OldJohn I really love Jonas's current hairdo though!

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.

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

user19161
@DavidWheeler I have never failed to be amazed by the stupidity and evil of mankind.
2

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

@MichaelGreinecker WTF??

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

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!)

@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...

user19161
@OldJohn I think many people in this room have pets.

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

10:06 PM
@DavidWheeler Two things are infinite: the universe and human stupidity; and I'm not sure about the universe!

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

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

user19161
@skullpatrol Was that from Einstein?

I'm not sure that glam-cleavage shock do much to naturalize sexuality. It's the overfucked-but-undersexed thing.
2

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

10:09 PM
@JasperLoy Yep.

@HenryT.Horton Hi ,Henry!

Holas... How did you find me

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

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

good evening all

10:13 PM
hi

good evening

Hello!

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

@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"

you were suspended for a "cleavage" avatar?

10:15 PM
Yep

@David No prob.

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

@mixedmath may 16

Did you mark it on your calender :-D
LOL

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

10:18 PM
@MichaelGreinecker Ah - you were the one that flagged him?
that's a funny circle

@mixedmath yes.

A Vienna circle :-D

user19161
A circular circle.

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?

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.

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.

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.

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

I was thinking about doing that, especially if it is, in fact, against the community norm
or perhaps I'd raise something on meta

Do we even have a Norm in the community?

there's tentaclenorm
one mustn't forget tentacles

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

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.

@JasperLoy No problem, J.
@JonasTeuwen Dude.
Dude.
Dude. Really.

user19161
@PeterTamaroff What, three dudes!

10:34 PM
@JonasTeuwen Looks neat

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

@DavidWheeler Thanks man!

@DavidWheeler HAHHAAHAHHAHAHAHAHAHHAAH

user19161
@JonasTeuwen Wow, you are the most cool looking guy there.

@JasperLoy Thanks.

10:35 PM
@JasperLoy This is important. Three "Dudes" is like DEFCON 5

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

@JonasTeuwen Jasper, I have a problem here.

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

@OldJohn Hmm... 8-).

user19161
My hair is so short that I look like a recruit.

10:38 PM
(as I get older gravity takes its toll)

user19161
I should try to take a pic this week.

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

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

@DavidWheeler OK. But now Willard is say this:

user19161
@jonas Did you see my announcement above that Debian is changing default to XFCE?

10:42 PM
@JasperLoy No.

user19161
@JonasTeuwen This has SHOCKED me!

@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!

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

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

10:44 PM

@MichaelGreinecker I have my copy here ...

@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??

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.

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

10:47 PM
@JasperLoy exacttly

any basis is already a sub-basis

@DavidWheeler Right. digs a hole

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

@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?

@OldJohn Do it for the LULZ.

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

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

@PeterTamaroff :)

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

@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.

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

10:52 PM
that's just the product topology

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

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

@OldJohn Why?? :-(.
@OldJohn Four spaces, right?

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

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

10:54 PM
@JonasTeuwen it would be nice if everyone agreed - but they don't :(
2, 4, 8 seem to be popular choices

@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.

@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 :(

@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.

@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

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).

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

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

@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!

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

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

11:02 PM
@MarianoSuárez-Alvarez Do as you wish...

I usually do

usually the strong topology is used for the quotient topology, because you are given q (the surjection), rather than an induced map.
well, i ask you: what is convergence?

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

@MarianoSuárez-Alvarez What did you mean?
@DavidWheeler I usually think about it in terms of nbhs.

11:06 PM
an element of a product can be viewed as a function (from the set of indices)

@MarianoSuárez-Alvarez Yes.

the usual topology of the produc t is that of pointwise convergence
when you view its elements as functions

the point i'm trying to get at: is that usually we speak of convergence of "sequences"
which is a function $f:\Bbb N \to X$

@DavidWheeler Right. That is what Mariano is saying.
(I guess =P)

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

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!

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

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

@MarianoSuárez-Alvarez True.

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

@DavidWheeler Yes.

11:14 PM

@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?

of course it has to do with that
because that is more or less the definition of the product topology

@MarianoSuárez-Alvarez I supposed.
@MarianoSuárez-Alvarez Yes.

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

@MarianoSuárez-Alvarez Hehehe well...

11:15 PM
@JonasTeuwen APIs are great - until they change the rules without telling you :)

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

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

@JonasTeuwen ROFL!!

@OldJohn 8-).

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

11:20 PM
@OldJohn DROP; 8-).

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)

Oh > 0...

I only deal with the ones who have a clue :)
Time I went unconscious for a few hours - later folks

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

@OldJohn Bye!

11:26 PM
@JonasTeuwen Bye

@OldJohn Bye :-).

@OldJohn bye
@MarianoSuárez-Alvarez Hey
I posted an answer to one of your questions on MO :D

I saw :-)

@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 $T(M)$

bazooka

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

That argumen is actually not quite absurd, really

@MarianoSuárez-Alvarez how come?
have you seen it before?

@BenjaLim what is $\alpha$ indexed by?

@DavidWheeler some index set
not necessarily countable, or whatever

@MarianoSuárez-Alvarez Bezouka!

11:35 PM
My objection, Ben, would be more that it is more of a detour than an awfully sophisticated proof

@MarianoSuárez-Alvarez :(
@MarianoSuárez-Alvarez I thought it was sophisticated enough

@BenjaLim i'm not convinced that U is open

@DavidWheeler I am told by my lecturer it is.

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

@MarianoSuárez-Alvarez Can you help to answer this

11:38 PM
Using theory about "solvability of permutation groups" or something like that.
No idea what it is though.

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

@PeterTamaroff you need to learn about groups

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

@DavidWheeler I don't know.
Not stated at all.

@BenjaLim, show that the set is in fact discrete

11:39 PM
what is?

indeed, the interior of each cell is an open set in the space
and that gives you disjoint open neighborhoods

@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.

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

Ok. So I need to be careful in selecting my $y_\alpha$. Fair enough.
2nd question

@MarianoSuárez-Alvarez Here

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

you are only attaching cells on their boundaries

@MarianoSuárez-Alvarez really?

well, if you are not, then you should
the attaching maps are defined on the boundary of the cells

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..

well, if this is an abrirary attachement, then no
CW-complexes, usually, are built in steps
attaching all n-cells at the same time

11:45 PM
hmmmmmmmm

so in that case the interiores are disjoint

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

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

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

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?

11:47 PM
dunno

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

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?

I would suggest doing both at the same time, mostly
simplicial complexes are regular cw-complexes

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

user19161
11:57 PM
@DavidWheeler A text he really hates.

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

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

yes
ALWAYS do that

In that case I think it should be easy enough.

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

11:58 PM
consider the simplest possible sitation

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

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