user19161
12:00 AM
@HenryT.Horton I am back, but I did click on leave all rooms. It does not work.

It is 2AM, let's go to bed early for once.
Good night guys!

@JasperLoy I wish it did.

user19161
@JonasTeuwen Ding ding ding!

@JasperLoy DING!

user19161
@PeterTamaroff I know, but how does this make it suffice to prove the result for open balls? It does not follow. Also, strictly speaking, the ball may contain only one point, namely a itself.

12:11 AM
@JasperLoy Yes, you're right. I think Hentry thought about neighborhoods in topological spaces which are open sets.
And considered that open balls form a basis for the open sets in my metric setting,

user19161
@PeterTamaroff There are over 9000 different definitions of nbhds anyway! But really my point is a general one: sometime we think A implies B when in fact A does not really imply B.

user19161
@PeterTamaroff So I suggest you try to prove it from the definition of nbhd directly and not use handwaving arguments like it suffices ....

@JasperLoy I already told you I proved the $\iff$ statement in one direction, but I'm stuck in proving it in the other direction.

user19161
@PeterTamaroff Are you sure you did it completely for that direction? I thought you only showed that direction for the ball and not the nbhd.

@JasperLoy No, no. I proved that if there is a neighborhood $N$ of $a$ in $X$ then $N\cap Y=N'$ is a bnhd of $a$ in $Y$.
It follows very easily because if $B_X(a;\delta)\subset N$, then $B_Y(a;\delta)\subset N\cap Y=N'$

user19161
12:17 AM
@PeterTamaroff Your definition of nbhd of a is a set containing an open ball with a right?

@JasperLoy Yes. A set $N$ containing an open ball about $a$.

user19161
@PeterTamaroff Yes, that is what we talked about just now, but that itself is not enough to prove that direction, since the B's are balls and not nbhds.

@JasperLoy But, silly! If $B_Y(a;\delta)\subset N'$, then $N'$ is a nbhd of $a$ in $Y$!

user19161
@PeterTamaroff I think I mixed up your two directions, let me read the transcript again!

user19161
@PeterTamaroff Ah OK, sorry I thought you proved the direction you did not prove, sorry!

user19161
12:25 AM
@PeterTamaroff I will give you a hint for the direction you are trying to prove now. You have done it for the ball. Now there are points in the nbhd outside that ball. Try to use these points to form a neighbourhood with the corresponding other ball.

@MarianoSuárez-Alvarez Esuchaste del concurso Zurich Clarin para mejorar la educacion en la secundaria de Matematica?

Entregan $250.000 en premios Que obviamente son para financiar los proyectos educativos. 3 de los cinco jurados son (no por casualidad) de la UBA Nunca habia ni escuchado el nombre del premio :) Me parece algo muy bueno, considerando el estado de la educacion en matematica 12:39 AM depende de qué sea lo que terminen premiando lamayor parte de lo que llevo visto en mi vida hecho "por la educación matemática" siempre fue catastrófico @MarianoSuárez-Alvarez mmmm que mal bueno, ya me habias contado sobre la curricula de analisis I @MarianoSuárez-Alvarez Justo ayer le estaba contando a un Brian Scott que le tuve que enseñar la aritmetica de fracciones a una chica de 14 años que tiene matematica previa.... imaginate! No es solo en Brasil que la educacion de matematica es pesima? Does anyone know how to represent the "without bound" symbol on mac/linux? 12:45 AM @MeAndMath No solo en Brasil! @MeAndMath Could you work out that topology problem? user19161 @peter Still can't get that direction? @PeterTamaroff Que situación lamentable...Yes.Thanks for helping! @JasperLoy I didn't try yet. I was too busy eating brownies. With merengue and dulce de leche, which kinda makes the point. Actually..I have a test in a couple of days....nervous. @MeAndMath Chillax, dude. user19161 12:47 AM @PeterTamaroff Oh OK. I think you can do it, you just need to spend more time thinking. @PeterTamaroff At this point,it´s hard @MeAndMath When are you having the test? next monday... user19161 @PeterTamaroff Somehow that looks a bit like you, hehe. 12:48 AM @JasperLoy What? user19161 @PeterTamaroff Well, I see that they are topologically equivalent! @PeterTamaroff I´ve been studying so hard...I spent the whole month studying. @MeAndMath But when is the test? user19161 @MeAndMath What topic is it? @PeterTamaroff next monday. 12:51 AM @JasperLoy Real analysis:sequences,topology in the real line,continuous functions... @MeAndMath Do you happen to have a mock paper to see? @PeterTamaroff I´ts in portuguese,do you mind? @MeAndMath I might be able to manage. http://www.ime.usp.br/~tausk/texts/PSubMAT0206-2011-Gabarito.pdf It has the answers.I couldn´t find only questions... 12:54 AM What is "valor de aderencia"¿ @PeterTamaroff It is the limit of a subsequence @MeAndMath Oh, OK. Suponha por absurdo @HenryT.Horton Do you speak portuguese? @MeAndMath And given$U$, what do you denote by$\partial U$? 12:56 AM @PeterTamaroff Is the set of the boundary points @MeAndMath Não @MeAndMath Oh,$\operatorname{Bdry(U)}$? Surely your notation is cooler. Everyone uses$\partial U$, Peter... what kind of books are you reading @MarianoSuárez-Alvarez I got my driver's license now, so I might be able to make a visit to you some time in August, maybe. @PeterTamaroff yes.... user19161 12:58 AM Even boundary can have slightly different definitions. @HenryT.Horton XD Introduction to Topology by Mendelson. But what does$\partial$have to do with "boundary"? @PeterTamaroff I really tried to do this exercise...but i couldn´t....Are you undertanding the questions? @PeterTamaroff, cool :-) @PeterTamaroff I don´t know either just drop me a message, to check that I'll be there 1:00 AM @MarianoSuárez-Alvarez OK. But a message where? @MarianoSuárez-Alvarez OK. I'm still expecting yours =D Yeah :/ Maybe you'll like the english version better, because in the spanish one I sent you I went into some details of convergence and made silly mistakes. user19161 @PeterTamaroff Oh congrats! I don't have a pilot's licence but I can fly to see you in my dreams. 1:04 AM user19161 @PeterTamaroff At first I thought that was from Aviator. @MeAndMath I think 1,2,3 are very doable. I don't know about$4$though. Maybe you can use that any open subset of$\Bbb R$is indeed an open interval. @PeterTamaroff Yes.I think that too.couldn´t do the fourth either Did you see how it was solved? Then its boundary is$\{a,b\}$where$U=(a,b)$I don't know the definition of interior though. user19161 @PeterTamaroff A subset of R is open if and only if it is a countable disjoint union of open intervals. This is Lindelof's result. user19161 1:07 AM Of course the same result does not hold in higher dimensions. I know it can be proven that$\partial U=\overline A\cap \overline {A^c}$@JasperLoy Good to know. I'm barely starting with the topological spaces chapter now. @PeterTamaroff Yes ,yes.See if this def. you can understand:en.wikipedia.org/wiki/Interior_(topology) Hey @PeterTamaroff ,This concepts are in \mathbb{R} @MeAndMath Ok. You can show that now ball around$a$or$b$is contained in$\{a,b\}$maybe? That is,$\{a,b\}$has no interior points. @PeterTamaroff Didn´´t get the point... oh I did! It´s possible i think I don't know if you can use what Jasper is saying about Lindeloff, though. @JasperLoy I was reading about guys in Topology yesterday: Lindeloff, Hausdorff, Alexandroff. I fit in perfectly. user19161 1:12 AM @PeterTamaroff Hahahahaha. @PeterTamaroff No,Pete,I can´t... @MeAndMath Heads up: "pete" in Argentina means BJ.... and no, it is not particularily Bieber, Justin. SORRY!!!!what is BJ? 3 user19161 @MeAndMath Er... @MeAndMath How do I make it child safe?? "sugar um garoto?" 1:15 AM Hi guys! @PeterTamaroff I´m not understanding.... user19161 @PeterTamaroff Also for the Russians Shilov, Kolmogorov, Novikov and you with spelling modified. Boquete @JasperLoy I'm seriously thinking about changing my surname to Tamaro v @HenryT.Horton blowjob oh.. 1:16 AM @MeAndMath WATCH YOUR MOUTH Literally In fact Alexandroff is Alexandrov. It is just romanized by most people. @MeAndMath Note that @PeterTamaroff Can you help me with a insight in Complex Analysis, please? It is Needham's book getting my head wrapped... @IanMateus I don't know if I can. But shoot. @MeAndMath Note that in the proof by contradiction Por absurdo @PeterTamaroff it must be easy, it is an exercise 1:19 AM @IanMateus já tá na análise complexa,Ian ? @MeAndMath do you know me? they are assuming there is an interior point$x$, so there is an open ball$(x-\epsilon,x+\epsilon)\subset \partial U$@PeterTamaroff yes @IanMateus Não. @MeAndMath And they show this leads to a contradiction @PeterTamaroff First exercise, ii. It asks for a geometrical reason of the substituition$X = \left(x - \frac{-A}{3}\right)$1:20 AM Because since$U$is open, it is disjoint with its boundary. @IanMateus More context. @PeterTamaroff Oh!got it! What is$X$, what is$A$? @MeAndMath didn't want to be rude, it is because I think there's a friend of mine at this community @PeterTamaroff Where ?In what part?usually is a set... @IanMateus sim,sim.claro. @PeterTamaroff do you have a PDF of the book with you? 1:23 AM @IanMateus Not really. But I guess I can get one in no time. @IanMateus I have! the topology one? mendelson? @MeAndMath No no, Needham. @PeterTamaroff Not having English as first language embarrasses me sometimes... @MeAndMath are you Brazilian? @IanMateus That is very, very silly. @IanMateus sim 1:24 AM What is your first language? @PeterTamaroff Portuguese. @PeterTamaroff anatically it is very easy to see, but I couldn't see geometrically @IanMateus LOL @MeAndMath que estado? Eu sou do Pará Usually it is the other way around! @IanMateus vish!Sampa. 1:25 AM @PeterTamaroff =( @IanMateus Nah! Could you give me a link to the file? So I can see @PeterTamaroff I think it is incredibly ridiculous, I know hah @PeterTamaroff how can I send links? I saw someone sayting not to just drop it saying* @MeAndMath Faculdade? @IanMateus [description](link) @IanMateus sim.tô. 1:28 AM @PeterTamaroff so,Peter,is there anything else that you don´t know definition or something? @MeAndMath Qual? De matemática mesmo ou engenharia, fisica...? @MeAndMath Well, in general I know nothing about Topological Spaces. Matemática aplicada..tá na descrição All that I know is Metric Spaces. @IanMateus Page? @PeterTamaroff this is easier because is everithing in a line,th real... 1:30 AM @MeAndMath Yes, I see. @PeterTamaroff 45 What is your career? @MeAndMath sorte sua! Ainda tô preso no segundo ano @PeterTamaroff is it with me? Those are nice exercises! @MeAndMath Actually, both- 1:31 AM @IanMateus o ensino é bom? @PeterTamaroff it is funny because I had no problems with another questions @MeAndMath regular. Eu que estudo sozinho mesmo I´m still studying.It´s funny ,but I have to chose a carreer after graduation.I like dinamical systems,graph theory,PDE... @IanMateus For$1.$just use derivatives. @PeterTamaroff yes, the second one specifically @PeterTamaroff I just couldn't see the "depressed cubic" at the graph Wait, wrong words. Let me try and think how to say it. Well yes. 1:34 AM @PeterTamaroff ok @IanMateus Jesus,Ian,you scared me!you are seeing the complex arithmetic part..I thought you were in the complex analysis part already! You're basically making your cubic anti symmetric about the$y$axis. @MeAndMath but that's the plan lol I've been reading Real Analysis books too @IanMateus Good!!!REally good!!! @PeterTamaroff really? I couldn't see it. Maybe because of the first derivative being a parabola? 1:37 AM @IanMateus Do you have GeoGebra? @PeterTamaroff yes! @IanMateus Great, I'll give you a file. @PeterTamaroff thanks! I just didn't want to ask it normally in Math.SE @IanMateus sabe,essas coisas são meio chatas:nesse país se você não estuda sozinho,com o que se aprende na escola não dá pra chegar nem na metade... @MeAndMath verdade. Sou apaixonado por matemática 1:40 AM @IanMateus Here . @IanMateus É?Isso é maravilhoso!mas aposto que para o que você sabe e quer saber não há investimento... @PeterTamaroff please, could you show me a example when the cubic has just one real root? I had seen$-A$as the sum of the roots and$\frac{-A}{3} as the aritmethic (word I've just forgotten)

@IanMateus $x^3-1=0$?

@PeterTamaroff mean. That's the word

@IanMateus I didn't understand your question!
=)

1:46 AM
@PeterTamaroff nevermind, I just realized a thing looking at the graph. Thanks! Time of studying now :D

@IanMateus Did you make use of the geogebra thing?

@PeterTamaroff yes!

@PeterTamaroff A stupid question,that is not pertinent to the chat,but is there very cold?

@MeAndMath It had been cold, but now it is not that cold.
Though there were days when the grass and the cars got covered in thin ice.

@PeterTamaroff Oh.Nice!Here is a little cold,too.maybe snows in the south.

1:54 AM
@MeAndMath It didn't know you had snow! We dont.

@PeterTamaroff in the states in the south of country ,sometimes,when is real cold,snows.
what part of Argentina are you from?

@MeAndMath Buenos Aires.

@PeterTamaroff Cool!!!

@MeAndMath I guess it is.
@MarianoSuárez-Alvarez How would you tell someone what topology is in "one sentence"?

This is hard...but this someone is non mathematical?

2:04 AM
@MeAndMath Yes.

You know,usually when I have to do these things,people ask me to stop...

@MeAndMath Hahahah

@PeterTamaroff hey, one more thing, please! Could you explain me a bit about how Galois developed the idea of a non-solvable by radicals polynomial? I've read some articles, but they were just too... abstract and I would ask you for a informal approach (if it is not much, of course)

@PeterTamaroff then I use the standard answer:It studies a lot of things,it´s abstract and "ordinary people" usually don´t use it...

@MeAndMath hahaha you have a link?
@IanMateus I honestly have no knowledge of Galois Theory.

2:12 AM
@PeterTamaroff oh, ok!

@PeterTamaroff it´s a litlle silly,talks about more about the geometric part,but i think it´s funny.

@MeAndMath I answered it is the study of the continuous.

@MeAndMath hey, do you know opportunities of work to mathematicians here in Brazil?

@IanMateus yes,in universities,other places..you ask if you have jobs for mathematicians?

@MeAndMath some career to grow into it

2:17 AM
@IanMateus Yes there is.
you,know,it´s a hard subject...

@MeAndMath can you give me some examples? I am truly interested

@IanMateus well,it depends.what would you like to do?where would you like to study?

@MeAndMath I'd like to study Mathematics at UFRJ (or, if I'm really lucky, aerospace engineering at ITA...)

@IanMateus no ITA...é bem difícil,mas não impossível e você teria que viajar,né...mas vá em frente.

@MeAndMath Viajar não é um problema. O problema é passar
@MeAndMath Odeio química heh

2:23 AM
@IanMateus se é...cai química,né...

@MeAndMath sim
@MeAndMath however, gotta go. Bye!

@IanMateus boa noite!!!
hey!this question could anyone give a light?it doesn´t seem to be hard...

2:42 AM
@PeterTamaroff, don't explain what a a topology is: explain what a metric is

@MarianoSuárez-Alvarez Yes, that would be easier.
@MarianoSuárez-Alvarez Mariano, how long have you been in the CONICET?

I had a scholarship years ago
and i have been an official research member since january

@MarianoSuárez-Alvarez Oh, congrats on that.

yeah, it is pretty cool :-)

I've heard it was doing better than someother years.
It is true?

2:47 AM
yes

@MarianoSuárez-Alvarez In what matters?

in recent years it started hiring people again, after a longtime
there are more phd scholarships nowadays
when I got mine, it was pretty difficult to get one
now, it is reasomable

Oh. That is really good to know!
@MarianoSuárez-Alvarez Well, with a 9,88 average!

grades are a very relativ thing...

@MarianoSuárez-Alvarez Well, you're right.
But it still is impressive, IMO.
@MarianoSuárez-Alvarez Did you take any exams recently?
My friends had the final exam of Analisis yesterday

2:56 AM
a week ago or so

@MarianoSuárez-Alvarez Differential Topology?

differential geometry

Oh, right.
It is something like analytic geometry?

not really
:-)
you'll find out soon enough

=) I should get used to that answer.
@MarianoSuárez-Alvarez Guess so.
In what year is that taken?

3:00 AM
it is one of the last subjects you take
because it depends on other things

@MarianoSuárez-Alvarez The not so soon enough :P

@MarianoSuárez-Alvarez last?

don't try to go too fast
@MeAndMath, hm?

@MarianoSuárez-Alvarez you said it is one of the last subjects...

3:02 AM
@MarianoSuárez-Alvarez Yes, I know. I usually try and step back if I find myself in a "no end street", so to speak.

@MeAndMath, I know;l but I do not know what you intended to ask with that «last?»

@MarianoSuárez-Alvarez It´s because in my University it isn´t one of the last subject.We study it in the second year.it comes before topology.

well
this subject is differential topology of manifolds, de rham cohomology and riemannian geometry on manifolds
the title is pretty much irrelevant in determing what a course is about!

@MarianoSuárez-Alvarez ok!

to do differential geometry of curves one needs very very little calculus
to do surfaces, linear algebra is pretty much needed

3:07 AM
@MarianoSuárez-Alvarez that´s what I meant

but if you do that earlier, you can do all that in a 2nd year course without problems

@MarianoSuárez-Alvarez that´s case here.it´s in the first year,so,no problems
for some reason ,in my course this topic is not necessary...
it´s not the "must do"

3:29 AM
Well,it´s late...Good night everyone!

Nevermind
Whitney Grossztein theorem?