citedcorpse

ah yeah, it's an easy mistake to make

{a} will be a neighbourhood of a only when {a} is an open set, and that's definitely not always the case

not quite. you need every point to have a compact neighbourhood

terry tao has a writeup on his blog i think where he discusses how compactness is a generalisation of finiteness

every space. once you have an open cover of {a}, you know at least one of the sets contains a. hence you can just choose that as a finite cover

(the application is the thurston norm in 3-manifold topology. it has a lot of information, and we know it is always a rational polytopal norm. of course, the issue is that we don't know how to compute it exactly... even bounds can be tough)

just think about R^2 at first. imagine you have an oracle to compute the norm, and you know the unit norm ball is a rational polytope a priori. can you come up with an algorithm to determine the vertices in finite time?

it's a basic fact that norms on R^n are all equivalent. but some of them are more finitary than others: suppose the unit norm ball (which specifies the norm) is a polytope with coordinates lying in Q^n (a rational polytope)

so, here's an interesting thing

and normally i like CW spaces... :P

@anon ah of course, i forgot. woops

is it not uncommon for there to be reputation lag?

they will be a countable union of open balls though

@Lord_Farin repeatedly claiming that you're taking an objective standpoint doesn't actually do anything to strengthen your argument

the main important part ist he stuff in front of the y and its derivatives

yes, that's the terminology

kind of like the difference between solving Ax = 0 and Ax = b

with the e(t), it's inhomogenous

no e(t) means you call it homogenous (linear)

if you don't have the e(t), it's fine right?

hang on

which particular book is it?

drop the g(y) and it's fine

urgh, i am clearly very drunk, sorry

woops, yep

"linear in x" would mean something like f(x,y) = ax + g(y), where g is some other function

well, if it just says "linear" then what i've written would probably be the usual interpretation

@nerdy you can talk about both. f(x,y) would have the form f(x,y) = ax + by, where a and b are constants

the usual definition takes as a basic concept "open sets", and says that "the preimage of an open set is open". a lot of people get confused why it isn't the other way around

then a continuous function, in this formalism, says "a continuous map maps close points to close points"

basically there's a version of the definition (equivalent, of course) of a topological space in terms of a "closure operator"

i think the two most basic notions to get acclimated with is "sets are not doors" (they can be both open and closed) and the definition (or characterisation, depending on your axiomitisation) of continuity in terms of "closeness"

formally, it's with respect to X and its induced topology

let's not think too critically about that sentence

even the best make mistakes, i made a mistake, therefore i am the best

sorry about that

@amwhy hah wow so reading comprehension is not really My Thing

or err, it's only a grothendieck prime

@amWhy 77 is not a prime

well, an analogous example (text: books :: actors : movies) is the general male dominance in films. you might like to read about the bechdel test, for instance

such a directive would be fine! it's more about "not seeing yourself" in the things you read

that's a pretty interesting idea @amWhy

i've seen a lot worse things in maths departments, but for this site it's the only hurdle i can think of

it was feeling a little lonely on that thread

Thank you sir! (i kid, i kid)

the mspaint diagram you mean?

(i don't know any lie stuff)

that was wittier in my head

ask me no questions, i'll tell no Lies

notionally, i'm here in budapest but i've had to take a break (woo mental illness)