@JM I totally agree. A good answer is more than the idea behind it. =)

And if Gortaur hadn't seen the discussion in the chat, there was absolutely no need to make it CW...

no way )

@J.M. I had a question about accents. I understand the meaning and need for the accent in Poincaré. But what does it do in Bézout or Bézier? Should I elongate the vowel sound while pronouncing the word?

Just thought you might know the answer...

Well, sans accent, it just sounds like "BEH-".

Er, that's how I pronounce with the accent. =) What's the right way?

With the accent, there's a hint of a long vowel.

Somewhat like "BEHY-"

But only a hint of the "y"

where does your garden grow?

Put another way, it's in between the "a" and "e" in "laser".

@JM Um, I tried the variations. But these distinctions just seem smaller than the least count of my tongue. =) // Thanks for the explanation though. :)

@Srivatsan: ask Didier ;)

Going back to ol' Henri: it's not quite "PWAN-kah-reh" and not quite "PWAN-kah-ray"... it's in between.

(If it's any consolation, it took me a while to get used to pronouncing properly.)

Is it fancy to use \gt instead of > ?

@JM I always wondered why English speakers are adding those "hints" of y to french e-aigu (they tend to exaggerate this a lot). To my (not quite native) ears it sounds way better without any such hint.

@tb: hi

(than with an exaggerated one)

@Gortaur: hi.

@JM But it's better than rhyming it with "loin care", I hope... =)

@Gortaur The problem is that < and > may interfere with the display on the page since the parser sometimes mis-interprets them as opening a HTML tag.

(what follows may be swallowed by the engine)

@tb Is é even supposed to be a diphtong in French?

@tb Not quite sure. But the guy who taught me French made me do all those tongue gymnastics... :D

@tb icic

He made it a point to say to say "not a 'long a', nor a 'long e'..."

@HenningMakholm No, definitely not. Because it is usually quite long, the é may get a tiny little bit closer to an i towards the end of the pronunciation but hardly discernible, I think.

(Man, it's hard to discuss pronunciation in chat... :D )

Well, maybe this helps :)

as usual, encouraging music

I was expecting the first phrase to be London is the capital of Great Britain

My taylor is rich...

After repeating the sounds in that YouTube demo, my nose feels funny... :D

@JM: do you want me to look for -ion, -en, -an, -ein, -in, etc? :D

Oh boy... :D

Interestingly, I hear the "eu" part as one vowel in the é/eu examples, and a consistently different vowel in the è/eu examples.

Perhaps a side effect of being modified by a subsequent /r/.

sumatra pdf is much more convenient to work with, but in Acrobat Reader it's more comfortable to read the text, strange

It's ClearType. Adobe's patented :( technology...

I thought it's supported by Windows in any application

Perhaps a laxative would help.

nez noeund

the french are strange people...

@Alexei: good evening

yo

@Gortaur Ack, sorry; ClearType is MS's technology. I forgot the name Adobe gave to their algorithms...

my desire to learn french has just evaporated :D

@AlexeiAverchenko how did you read War and Peace without knowing French o_0?

i didn't :)

@Gortaur I believe books can be translated nowadays.

@AlexeiAverchenko shoolota :-p

i hate most russian classics, they're written by neurotics for neurotics, and then interpreted by psychotics to mean whatever they fucking want them to mean.

@AsafKaragila It just ain't the same, y'know? ;)

@AsafKaragila in the original version all the letters are in French. And there are over 9000 of these letters

@AlexeiAverchenko me too. You remember? Author would like to say

...I gather the classes you guys took on Russian literature were a PITA...

I especially hate Dobrolyubov, who somehow managed to interpret obvious pagan motives as a statement of feminism

@JM לא, אני לא יודע :-)

@AsafKaragila I see some cardinal numbers in your sentence ;)

what's PITA?

@Gortaur Which part? The ":-)"? It means a smile, not a cardinal number.

@AlexeiAverchenko You seem to have something against paganism =)

i guess P stands for pointless, but other than that i'm totally ost

lost

@AlexeiAverchenko Either Pain In The Ass, or a kind of bread which Israelis eat a lot.

@AlexeiAverchenko Greek fastfood which gives you pain in the ass

@Srivatsan not really, in many respects they're much saner than monotheists

Put it this way: idioms and "style" (whatever it could possibly mean in the context of writing) don't always hold well after translation...

@AlexeiAverchenko who the hell is Dobrolyobov? I know only Belinsky, he was a cool critic

Добролюбов

о, почитай

@AsafKaragila nope, א

особенно с вставками Жданова

@Alexei: he was revolutionary democrat? hate those revolutioners

i do love Mayakovsky, though

@Gortaur he was the guy in charge of culture under Stalin

you can guess the rest

am I what?

shame on me, she was Yesenin's wife

fuck Yesenin!

notice how I bring high culture to this chat? :)

How do you do that to a dead guy? ;)

@JM what would you expect from the anime guy like Alexei? ))

lol :D

@AlexeiAverchenko that's what Russian poetry is about: high culture and obscenity

personally I cannot understand why everybody there is so mad about Pushkin

even chrome's spellchecker knows him

Lermontov he does not know!

@Gortaur neither do i

he wrote about some boring adventures of some boring half-wit officer in Georgia

not exactly my kind of novel

Anyway, I was totally frustrated reading 'Golden Age' literature like Tolstoy, Dostoevsky etc. who were just chewing snots and encouraging 'Great Russian Revolution' instead of just saying people that without doing your job well you'll always be in a crap

I had a headache after "Crime and Punishment". That's normal, right?

absolutely normal

This guy and this guy must be classmates. They even refer to the same imageshack URL for their axioms.

@JM right. I was amazed by epilogue. Hollywood's Happy End should commit suicide after learning about it

it means you're real human

there's nothing more pathetic than some looney fanatic graphomaniac trying to be deep and psychological

@HenningMakholm Funny, that.

He is deep, but the point is that this literature is about thinking and reflecting - as if it was missing in Russia where almost everybody preferred (and still prefers) to think and reflect guessing What would be if...

@Gortaur The Russian Revolution doesn't count as action?

The closure of this L^\infty-question came surprisingly quick for me... It would have been nice if at least one of the voters had left an explanatory comment.

(since OP is completely new here)

i like Griboyedov, if only because he was just plainly satirizing nobles, without attempts at false depth

and he always hit the mark

@Srivatsan do you really want me to comment on it?

@Srivatsan which one? :P

Uh-oh...

@tb I saw 2 votes when I decided to vote. Turns out I clinched the closure =)

@AlexeiAverchenko I liked him as a person at least. Cliche to say, but among Russian writers I mostly like Bulgakov, not only because of MM but also because of White Guard

@Srivatsan You've stepped into a minefield. Good luck... ;)

imo 1917 was like this:

@Gortaur I don't know much about it. Long time back, I looked to the great revolutions in Europe, somewhat as an inspiration.

first liberals and mild socialists kicked useless moronic nobles out of power

but then it turned out they can't get anything important done

@AlexeiAverchenko Yes, I do not approve of what happened after the revolution. =)

spelling reform is nice and all, but not when millions are dying at a war that nobody wants and the injustices of the land distributions are too numerous to count

Marx, Lenin, Stalin and Trotsky are all rolling in their graves right now.

so on october 1917 bol'sheviks kindly asked them to get the fuck out

and for a moment they did

@Srivatsan Let me try to explain you. There were Tsars who were autocrats and most of whom didn't care about people. There was the class called intellegence (people of a high culture) and there were young hot-blood empty-brain revolutioners

@AsafKaragila Great, if we could wrap a solenoid on them, we'll have a nice energy source...

allowing bol'sheviks to sign peace with germany, enact a land reform and reform the government so that regions had more representation

[contd.] this intellegence thought how to tell the Tsar that things should go in a liberal way and they were dreaming about making TheGreatRussianRevolution. Only thinking. Meanwhile revolutioners were bombing everything and everybody and killed the only smart Tsar

@JM You saw the SMBC from a few days ago?

Yeah... :)

what happened after that is not as good

@Gortaur I was gonna say "deluded" instead of "empty-brain", but oh well... :) your formulation works, too.

@Gortaur, it's intelligentsia

@AlexeiAverchenko whatever

@Gortaur Nicholas II?

no

alexander II

@Srivatsan nope. Alexei told you

I am going away now. I will be making shakshuka in about an hour. If anyone happens to be around, feel free to join in.

not that he didn't deserve it :D

but the ones after him were much worse

@AlexeiAverchenko don't start it. I agree that others were much worse. Nicolas II is an unicum

you think his reforms were anything other than a joke?

@Gortaur Oh, ok. I didn't know about this pre-1917 Revolution revolution.

(Or may be I once knew.)

@JM Now I know what you mean =)

@Srivatsan ;)

@Srivatsan the trick is that as a result the power was taken neither by infantile intellegence nor by revolutioners, but by bolsheviks who are suspected to receive money from Russian's enemies (the WW I was going on that time)

btw i think even in their graves Stalin and Trotsky are rolling in the opposite directions :)

@Srivatsan It was in 1917, but earlier in the year. That's why the bolshevik revolution became known, specifically, as the October revolution.

@AlexeiAverchenko one is in opposite and the other is not

@HenningMakholm happened to be on 7th of November ;)

@Gortaur i don't think anyone cared

@AlexeiAverchenko ah?

@HenningMakholm Then who is this Tsar Alex II?

about the funding from the Kaiser

@Gortaur November, Gregorian. AFAIU it was before they got around to switching from Julian calendar.

@Srivatsan he was killed without revolution

@Srivatsan he is known for freeing the serfs

if you can call it that

although it was a step forward from having no rights at all

@HenningMakholm yeah, but that was funny that USSR was following Julian one and celebrated October revolution in November

@AlexeiAverchenko I do care

@AlexeiAverchenko I think I need a more elaborate history lesson then. I might as well go to wikipedia for details.

@Gortaur why?

Kaiser wanted to sign separate peace

nobody in russia wanted to continue the war

@AlexeiAverchenko this should be transparent. in the History textbook it should be written explicitly: Lenin was funded by Kaiser, so the whole October revolution was just a bullshit. Dot.

except for let-them-eat-cake nobles and i-guess-we-should-wait february guys :)

@AlexeiAverchenko Except, of course, that the old regime was honor-bound to keep there treaty obligations to Serbia and France.

@Gortaur first of all, it's period :) second, lenin never acted in kaiser interests

especially because kaiser lost his power very soon

because the germans didn't appreciate dying for nothing either

@AlexeiAverchenko yeap, Lenin was acting just by his own interests

Russian history is so messy, it's fascinating...

@Gortaur sure, that's what made him such a good leader :P

@Gortaur What's not in the history books? About the only thing everyone knows about Lenin is the sealed-train ride through Germany -- obviously it was in the German interest to support a Russian government that would agree to closing down the Eastern front.

@HenningMakholm 14-years old children do not necessary make such statements if it's not said explicitly

@HenningMakholm Nobody wanted to continue the war, but the war was to be finished with Russian to win. After October revolution Russia 1. betrayed France and others 2. lost the war

Why is complex projective n-sapce, defined by (C^(n+1)-{0})/C^*, Hausdorff? I looked in Munkres and he just says that in general, it's hard to find a condition that makes quotient spaces Hausdorff.

I bought some wine for the commission. Would it improve my grade if I gave it before my presentation?

No.

@JonasTeuwen nope. You're in the Netherlands

@JonasTeuwen What's the commission? Do you mean committee?

Damn non-corrupted people.

@Srivatsan Yes, sorry.

@JonasTeuwen You mean, dose them first before your presentation? That can be counterproductive...

Anyway, two of them are my colleagues now. I doubt that they will spare me :-/.

@JonasTeuwen I'm not sure that I will see you here before your defense, so I wish you to do it supercool

Thanks! :).

@Alexei: let us finish it now. That should be discussed with vodka on the table, otherwise there will no be any consensus

By the way Gortaur: you and Jonas have finally seen each other, no?

@JM aha

Yes we did.

anyway, I have to go. so see you all later. I'm totally angry now, too young to talk about revolution without getting angry

Angry?

See you!

@Gortaur sure they saved millions of lives, but being loyal to France - THAT's what's really important :\

Sorry, Gortaur. But thanks for the impromptu history course!

Oh, there has been a conversation before this. I'll stay out of that :-).

@JM are you kidding? no needs to sorry at all, I heated up myself myself

@AlexeiAverchenko breaking promises is indeed important

@JonasTeuwen Well, Srivatsan had no idea he was opening a can of worms... :)

@Gortaur, you should fix your priorities

listen to Mario Savio speech

he knows his stuff :)

How do people get this helpless?

should Lenin be of the first priority?

@Gortaur human lives and welfare should be

By golly! I've send an e-mail to the group that I'll have my final presentation tomorrow and I seem to have forgotten the hour.

@HenningMakholm Those people are there to make you feel less stupid :).

@AlexeiAverchenko of course. from 1917 to 1922 humans lives and welfare increased a lot. really a lot. bye ;)

@HenningMakholm Clearly his geometry was left behind for his calculus. A pity...

@JonasTeuwen I feel like reserving a hotel room in Stockholm already.

@Gortaur indeed they had, as was confirmed by the studies

but it's not really fair to get the civil war into it

compare it to the NEP years

or the early Stalin years

it was the time of social progress and economic growth while everybody else's economy was in shambles

Anyone algebraic geometers in here? I have a few simple questions on Rick Miranda's book.

@Potato sorry, can't help you with algebraic geometry

but i've got a quick question for the community

I've posted a question on here

it has no votes nor answers

Link?

i just found out that the same question has been already asked and answered on MathOverflow.com

should I delete my question

?

here are the links: my question: math.stackexchange.com/questions/82777/…

MO question/answer: mathoverflow.net/questions/75829/…

If it has a nice searchable title and description, I think a better solution would be to write an answer of your own, pointing to the MO thread and summarizing the solution.

i can't believe i didn't find the MO answer initially...

allright

@Bullmoose Don't worry; always happens. =)

for now I'll post the link to the MO answer in the comment

since i'm working on a paper, and since the deadline is 6 AM EST, which is about 15 hrs from now, i won't write a detailed answer quite yet

will later

the MO answer points to a keyword and comments contain reference to a book

thank you for help

@Srivatsan Sorry for the typo :-)

@MartinSleziak No problem, Martin. =)

I am not sure whether I should keep my answer too, but I am inclined to do so.

I asked about the name of the book specifically for the reason that I can check the formulation there.

But it is almost sure that the meaning from your answer was the one intended there.

Suppose a collection subsets U_\alpha of a set X is given. Define a topology on each U_\alpha. Define a topology on X by declaring a subset V open if and only if V intersect U_\alpha is open in U_\alpha for every \alpha. I have verified this is a topology. Question:

[If it's any consolation, my name has seen bigger typos. =)]

@MartinSleziak I don't know. To be honest, I didn't quite follow your solution. I didn't read it carefully enough.

Well the only difference is that you chose the usual measure on [0,1] and constructed a step function.

Suppose each U_alpha is connected. Form a graph with one vertex called v_\alpha for each U_\alpha, and with vertex v_\alpha connected to v_\beta iff U_\alpha intersect U_beta is nonempty. Prove or disprove: X is connected if and only if the graph is connected.

Could I get a hint for this? Not homework, just self study.

While I worked with the identity function and used a different measure to make the steps.

So it's obvious graph connected implies X connected, right?

What is U_alpha?

Neighborhoods?

See my prior chat at 14:26.

They are just subsets of X, which we then use to define a topology on X.

Martin: Oh, I took uniform measure over [0,1] and a step function. Your function is simpler (constant or identity?) but the measure is a combination of the Dirac measures. // Summarizing to myself basically.. :)

Yes, they are two facets of the same thing.

@Potato I can't find it. Link?

The uncountability is making this tricky. I want to say assume we have a separation U,V of X, and show this leads to a separation of the graph.

Suppose a collection subsets U_\alpha of a set X is given. Define a topology on each U_\alpha. Define a topology on X by declaring a subset V open if and only if V intersect U_\alpha is open in U_\alpha for every \alpha. I have verified this is a topology. Question:

Suppose each U_alpha is connected. Form a graph with one vertex called v_\alpha for each U_\alpha, and with vertex v_\alpha connected to v_\beta iff U_\alpha intersect U_beta is nonempty. Prove or disprove: X is connected if and only if the graph is connected.

I want to say take two of the U_\alpha, one in U, one in V, and show this leads to a contradiction, but I have a problem because the "path" of the graph joining of them my be uncountable.

@Srivatsan This is probably 14:26 in his timezone chat.stackexchange.com/transcript/message/2450870#2450870

Ah, I forgot we are all in different timezones. I restated everything above.

To be honest, I do not know how connectedness is defined for infinite graphs.

The same as for finite? Using finite paths?

Neither do I, which makes this problem tricky!

I can think of using connectedness from topology to define connectedness for a (potentially infinite) graph. What does that give us?

According to wikipeida, a path may be infinite.

although it's a sequence so it's necessarily countable

Ok, I thought that chain characterization of connectedness from this answer coud be useful: math.stackexchange.com/questions/44850/…

But I am not sure if this could help for infinite paths.

Wait, isn't a path from a point to another point always going to be finite?

I think so.

Ok then there's no problem.

You meant this wikipage, right? en.wikipedia.org/wiki/Path_%28graph_theory%29

We take a path from a U_\alpha in U to a U_

\alpha in V

and then we get a connected set, which contradicts separation.

It seems right to me.

So for the other way, we assume the space is connected, and the graph isn't

So there are two points in the graph we can't join by a path

For other direction, I believe that the answer I linked above could help.

Indeed. Let me look at it.

BTW this problem is taken from some book?

Sorry for the interruption: can anyone tell me if this fails to be a counterexample and why? X = [1,2] union [3,4] with the usual topology. U1 = [1,2], U2 = [3,4], U3=X all with the usual topology. (Should verify that this is indeed ok.) (v1, v3) is an edge and so is (v2, v3). So the graph is connected. But, clearly the original space is not.

// I have a feeling I am missing something.

Rick Miranda's "Riemann Surfaces and Algebraic Curves"

Ah Martin, but the U_\alpha aren't necessarily an open cover.

Answering myself: Of course, it doesn't work: U3 is not connected. :(

Its page 12 - here's google books link books.google.com/books?id=qjg6GOQaHNEC&pg=PA12

So I can do graph connected implies X connected, but not the other way.

For the other way, is it possible to speak of cuts in the graph that disconnects the graph into two components?

What do you mean?

@Potato I believe that for the other implication you can take Henno's chain lemma for the open cover U_alpha.

U_alpha isn't an open cover though

Oh, I see.

@Potato Sorry if I wasn't clear.

For example, if we take the real line, we can take the single U_1 (0,1) and define a topology using that, as in problem A on page 12 that you linked

where we use an arbitrary topology on (0,1)

So say we have two points, a,b in the graph, that we can't join by a path

consider the connected component of the graph containing a and the connected component of the graph containing b. These are disjoint by hypothesis.

But \bigcup_{\alpha\in C} U_\alpha will be open for every component C of the graph, right?

yes

but this doesn't necessarily partition the graph into disjoint open sets because the U_alpha may not be an open cover

Well I think you're done.

Why?

Ok almost done.

And thus we found a clopen subset.

Why?

Let U=\bigcup_{\alpha\in C} U_\alpha

The intersection U\cap U_alpha is either empty or the whole U_\alpha.

Depending on whether alpha is in C or not.

Right

This is correct, right?

The same is true for the complement X\U.

For all alphas it will be either the whole U_alpha or emptyset.

Indeed

So intersection of the complement with each U_alpha is open.

Complement is open, U is closed.

Ok so we take a connected component and wish to show the complement is open. The complement is open if and only if its intersection with every U_alpha is open. But this is now a trivial statement

right?

Yes.

Yes!

I am pretty convinced that it is true. (Although I might have missed something, it is not very common for me to work with infinite graphs.)

it is morally correct

The book is on Riemann Surfaces; I don't think it would introduce a problem that required knowledge of something obscure about infinite graphs

Could you give me a precise definition of "discrete subset" of the complex numbers. See problem D on the same page.

It seems plausible.

Does it just mean no limit points?

I would say that if I take subspace topology, I will get discrete subspace.

Equivalent: Each point is isolated.

ah ok, then the problem is trivial

Question D seems to be example of 2-dimensional lattice: en.wikipedia.org/wiki/Lattice_%28group%29

we just construct a sufficiently small epsilon and we are done.

It is probably good to notice that it suffices to show that 0 is isolated.

And to explain where the fact that w1, w2 are independent is used.

Err, how is that fact used?

For example it would not work for w1=1, w2=sqrt(2), but these two things are not linearly independent.

hmm yes but I am having problems making this precise

Me too.

Trying to think about the explanation.

Let our two vectors be w_1, w_2. Pick the one with smaller modulus, and let epsilon be half than that modulus. It suffices to show the ball around 0 with radius epsilon contains no point of the lattice.

I do not think this last claim is true for any choice of w1, w2.

Let's try w1=2, w2=2+i.

Than i belongs to the lattice.

And it has smaller modulus than w1 or w2.

we pick less than half the modulus of the smaller one

If I took 3 and 3+i, I would get lattice point smaller than one half of the modulus.

ooh, this is correct

So let's suppose that 0 is not isolated, so that it is a limit point

I'm trying to figure out why this contradicts linear independence

I've put here 3 pages of the book Stewart, Tall: Algebraic number theory and Fermat's last theorem

There should be proof of this result for n dimensions.

It's getting late here and I am getting tired. So I am afraid I will not be able to help.

Alas, I must go. I will review the proof later. Thank you!

Ok

Just check whether you cen download the images.

See you.

@Henning: math.stackexchange.com/questions/82829/how-can-i-prove-that-x-x

New duplicate of the old question. But this one seems to be better worded (the new question states a lemma that can be used that is missing from the other questions).

Huh, scratch that. This question seems a little different.