Maybe you can only have sections on hausdorff open sets

That doesn't really sound like what Hicks is saying

:-)

I don't think anyone in the UK has eaten high tea for decades. I sometimes wonder what image the rest of the world has of the UK. Probably one from 50 years ago.

@Kaumudi.H Yes, it's easy for us Brits to forget just how big India is.

We think cities are a long way away of they're more than 100 miles.

I'm sure the queen has high tea every day

@Kaumudi when is the exam? Will you get a chance to rest and recover before it?

@Slereah :-) I probably ought to say I don't think most people in the UK have eaten high tea for decades.

I think from the east coast to the west India is about 2000 miles or something

@BalarkaSen doesn't that depend on the latitude? India being roughly triangular.

@JohnRennie Ya roughly I am thinking of West Bengal to Maharashtra.

@Kaumudi.H a day to recover then. At least there isn't any jet lag to contend with! Which exam is this?

Would you go there? Or is this mostly for practice in doing exams?

@JohnRennie It seems to me life is and was approximately the same everywhere, except in the currently nonexistent Soviet Russia, where communism exterminated bourgeois lifestyle.

Ah, the red days.

@Kaumudi what makes Kerala so bad? In the UK it is viewed as a popular tourist destination, mainly for the beach resorts.

@Kaumudi.H Why would your solcial life suffer from the language? Because you don't speak Malayalam as well as other languages?

throw it away in protest

@Kaumudi.H You're an ungrateful so and so :-)

It was nice of the school to go to the trouble of having the plaque made.

Personally I'd have preferred a few hundred pounds or even a laptop or two, but there you go ...

→ 1 message moved to Trash

@Kaumudi.H Done!

Even though a Keralan college wouldn't be your first choice it's always worth having a backup plan.

@blue Snif and a tear for those days, comrade, snif and a tear.

I'm pretty sure BalarkaSen is an old Soviet philosopher trapped in our time by some freak accident

I'm sure @Slereah will want to investigate this temporal accident

@Kaumudi.H My brother didn't get his first choice university and had to go to Imperial College. He was dismayed at first, but in the end he had a good time. I suspect wherever you go it will end up being a good time.

I am strongly anti-Soviet. Of course whatever I say here should be read with a highly satirical tone assumed.

@Kaumudi.H Most of us, when faced with having a good time or feeling down, will opt for the good time :-)

I knew a hungarian GR fellow

He had strong opinions anout communism

cool :P

@Kaumudi.H yes, and that was his second choice. My brother is a clever chap - possibly cleverer than me, though don't tell him I said so :-)

Wait, if according to Hicks, nonHausdorff manifolds admit a metric tensor but no metric

Is the same true for non paracompact manifolds?

vOv

Actually I think the long line admits no Riemannian metric

This is IIRC an exercise in Hirsch I didn't do

0celo7 can probably confirm.

I guess it has local sections since it's basically just R

What's the issue to form a global section?

Apparently the only vector field on the long line is the zero section

makes sense

Well the only smooth one

@AccidentalFourierTransform lol

will @0celouvsky lol too?

will @Slereah suggest to ban AFT?

Definately

Actually

I'm not sure Hicks ever actually says that non Hausdorff manifolds admit a riemannian metric

Just that he did not require it for his definition

Maybe that's the issue

The contradiction is just that they don't admit one, maybe

> chomolology

Typos are fun

Shlomology

"In order to be able to solve the wave equation, (M,g) must be globally hyperbolic and time orientable (cf Choquet Bruhat 1967)"

There's a whole bunch of GR papers from the same conference that aren't available online

The Battelle Rencontres conference

@BalarkaSen correct

By stone's theorem a metric space is paracomact

@Slereah that makes no sense

What signature?

@AccidentalFourierTransform wtf

@0celouvsky well, herés the thing

He says he does not define manifolds to be hausdorff

He derives that manifolds with a Riemannian metric define a pseudometric on the manifold

And that if it's Hausdorff, it is a metric

But I don't think he ever says that a non-Hausdorff manifold admits such a metric

So that might be the issue

@0celouvsky Why not? In a non-Hausdorff space, you can't "separate points", so it is conceivable that the usual way of defining the path length metric from the Riemannian metric tensor yields a pseudometric that assigns the distance 0 to these points.

@ACuriousMind see that theorem about T0 spaces

T0 + pseudometric = metric

"that theorem about T0 spaces"

And manifolds are T0

@ACuriousMind hmmm

@Slereah give link pls

euclid.ucc.ie/mckay/differential-geometry/hicks.pdf

Chap 6

p. 69 70

@Slereah Why not call them Kolmogorov spaces? I can never remember which $T_i$ is which

ACM might be right

I think you implicitly need to cover the two points with disjoint normal neighborhoods

Where?

Though I am guessing that this would fuck with the exponential map

@Slereah showing that the Riemannian distance function separates points

Well my issue isn't so much the distance function

Just the Riemann tensor

Is there a global section of $Sym(T^*M \times T^* M)$

yes, $0$

That's not a very good metric tensor

Of signature $(p,q)$

signature pq metrics exist sometimes

cf. Steenrod

Well does it exist at all for any p, q in a non hausdorff manifold

Say the branching real line

Man, I hate chemists. I never understand what they're talking about and every time I ask them "Can you put it in more basic terms for me?" they start saying just as complicated stuff only about hydroxide ions for some reason

lol, I love how my joke has been flagged twice

three times

@Fawad Care to explain what is rude or offensive about that post?

raise your hand if you didn't get the pun

@ACuriousMind iam chemist aspirant. He hates me :(

"He hates me" That's completely fine.

@Jim did

@Fawad I don't actually hate you. Clearly I'm making a bad chemistry joke

I'm a physicist, it's a requisite of the job

Alright

Well, I've popped my head in, offended some people, and completely failed to land a joke with the rest. I think my job is done for the day. See everyone some other time

@Fawad Well, that seems to have been a solution to the issue.

@Jim I hope this doesn't precipitate any hard feelings.

@rob hard feelings from me? Never. From others? Who knows

@Jim It is? I'll have to start writing "able to make bad jokes" on my resume from now on.

@rob Is that an intentional chemistry joke too?

::News from the future: ACuriousMind offered 30 jobs within 24 hours of posting revised resume::

@rob are made of copper and tellurium? Because you are CuTe

@Jim We've been trying to be careful in here about using salty language.

@BalarkaSen yes

Who the hell flags things anyway

I gotta say, I was skittish at first, but there seems to be real chemistry between all of us

@ACuriousMind Do you have access to springer.com/us/book/9783540011828 ?

@0celouvsky This ironic comment will probably stir up strongly polarized Fe lings.

I think this Hausdorff business will have to be a MO question

@Jim Yay!

@0celouvsky Yes

@ACuriousMind would you mind sending it to me?

it's nice to see people reacting so well to all these puns

I'm just ignoring you

@Jim One would expect, in a charged situation like this one, that equal numbers of the replies would be positive and negative.

This is an interesting query:

Users by total number of favorites on their posts

@DavidZ was in second place there

until I took out community wikis =P

@rob Indeed. Then I would have to worry about all of this corroding friendships

@Jim Look what we're reduced to here.

@EmilioPisanty w00t! I got #[error: Not identified on list]

@Jim Did you try looking beyond the top 50?

@EmilioPisanty I'm reasonably sure the two top positions are there simply because of their number of questions and because Qmechanic tends to star QM/QFT questions ;)

@rob On the plus side, it has formed a bond between us

@EmilioPisanty I got to 500 then gave up

@Jim But yeah, if you don't ask questions, what you get is <20 faves on your questions

oh this is by questions?

not also questions where you've placed an answer

@Jim yeah

makes sense

I suppose you could query for answers on questions with stars

but that feels like a stretch

@ACuriousMind ?

I take that as a no

never mind, Russian servers suffice

now that's just lazy

If you want the full demonstration check out Synge

He has a whole bloody chapter on the topic

Do you think it would be conceited to put "private correspondance" as a reference in a MO question

@0celouvsky Sorry, I was distracted. I gather you've already obtained it?

@ACuriousMind How is Kirchhoff (the German physicist) pronounced exactly? like kirshof, or...?

@Mostafa English does not really have the sound the -ch- makes, so I have trouble communicating the pronounciation

@blue These are all wrong

@blue That's also wrong

People say Car-shof. I think it'd be something like Kirk-hoff

@ACuriousMind They are automated pronunciation. Not reliable @blue

@ACuriousMind yes

@blue watch a movie

downfall

preferably

(removed)

@blue obsessed with Hitler? :o

@blue Der Untergang is a German movie

Hitler liked wildlife @ACuriousMind

@ACuriousMind Can I post Stalin speeches?

@0celouvsky What am I supposed to do with that information?

@blue Watch Goodbye Lenin...I liked it especially the music

@BalarkaSen I'd prefer to leave those out of here, too

lol

ah-hah!

Good alternative

@ACuriousMind that's a tall order

Trump speeches?

@blue oops

weren't you a trump supporter

@ACuriousMind Do Germans like mountain climbing a lot? Brad Pitt said in Inglorious Bastards.

a tarantino movie. ugh

To return to the pronounciation of Kirchhoff, maybe this helps: It's pronounced as it is written (with a short -o-), except for the -ch- which is a sound similar to the English sh except it is formed with your tongue a bit further back at the palate and with your teeth further apart so there's no "s component" to the sound

@BalarkaSen of course

Always will be

good

I assume kirch is pronounced like the drink

@Mostafa Uh. Some do, some don't.

He's not an intergalactic demon unlike most politicians

@Slereah What drink?

Might be kirsch

Like the cherry?

Yeah, if it's made from cherries it's Kirsch, not Kirch

And the -sch- is the same as the English sh, that one would have been easy to describe

The Kirch is not from the cherry, but from the German word for church

The Kirch-hof is literally the church yard

@ACuriousMind Wow interesting

@ACuriousMind you're missing the e

Oh, from

I misread

Ok I think I should leave before reaching the event horizon. Thanks for your help with the pronunciation (although I'm again confused, in another way) @ACuriousMind

Was Kirchhoff a German or a Russian

Hi guys

Think he was German