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/sci/ - Science & Math

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9766179 No.9766179 [Reply] [Original]

>talks about continuity without any reference to the topology

>> No.9766800
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9766800

>yfw there is a canonical topology

>> No.9768820

>>9766179
a gravitational wave is a continuous waveform and
having no topological space makes for good talks

>> No.9769090

>>9766179
>Objectively more useful and intuitive notion of continuity in metric spaces
>Brainlets insist on using the topological definition because of "muh generality"
Go away

>> No.9769107

>>9769090
In differential geometry, you must start with a topological space because there is no obvious way to asign it a usegul metric, and a lot can be done without mentionibg Riemannian manifolds.

>> No.9769736

>>9769090
>Replacing open set with open ball makes the definition more intuitive

>> No.9769759

I'm a physicist. All functions are continuous and differentiable.

>> No.9769796

>>9769090
The topological definition is way easier

>> No.9769813
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9769813

>>9766800
>literally any topological space has at least 2 topologies
>canonical

>> No.9770138

>>9769813
>{0} has more than one topology.

>> No.9770153

>>9766179
>lurk /sci/ for a day
>know that this is talking about non-euclidian geometry
I can feel my IQ points rising bros. Maybe a few years of lurking and reading books I might not be a brainlet anymore.

>> No.9770338
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9770338

>>9769759
Say what again?

>> No.9770407

>>9769107
>brainlet field for brainlet physicists
I'm kidding of course. Out of curiosity, what kinds of useful things are you talking about?
>>9769736
>brainlet topologist needs open balls to conceptualize a metric space
my sides

>> No.9770462

>>9770407
All the differential geometry that isn't riemannian geometry.

>> No.9770560

>>9769813
> thinking canonical means "the only"

>> No.9770972

>>9770560
I wouldn't even bother responding to them. 90% of /sci/ is fucking retarded like that.

>> No.9771071

>>9770153
dont know if this is master bait, but if it's not, then you're definitely retarded and wrong

>> No.9771306

>>9770560
>he thinks "canonical" means "standard"
*snap*

>> No.9773060
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9773060

>>9771306
that's literally what it means.

>> No.9773633
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9773633

>>9773060
>that's literally what it means
YIKES

>> No.9774299 [DELETED] 
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9774299

>>9766179
>a function is continuous as long as you never have to remove the pencil from the paper and there are no cusps

>> No.9774305
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9774305

>>9774299
>a cusp means the function isn't continuous

>> No.9774317
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9774317

>>9774299
>>9774305
>continuity implies smoothness

>> No.9774330

>>9773060
>>9773633
>it's another "animeposters argue semantics instead of discussing the actual math" episode
get a life

>> No.9774357

>>9770338
>Continuous in the discrete topology and differentiable in the weak sense
What's the problem?

>> No.9774431

>>9774357
>acting as if the dirac delta is a function
You played yourself. [math] \delta : S(\mathbb{R}) \to \mathbb{R} [/math] is already continuous with respect to the standard (read: useful) topology on the Schwartz space.

>> No.9774463
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9774463

>>9774330
>he thinks there's any "actual maths" in this thread ever

>> No.9774465

>>9774463
>implying you are not a faggot

>> No.9774509

>>9774431
Why schwartz though? Why not space of distributions? Who cares about what tails we have?

>> No.9774511

>>9774463
>implying that's not your fault

>> No.9774526

>>9774509
>Space of all distributions
Distrubtions are defined in function spaces you brainlet.

>> No.9774535
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9774535

>>9774509
The dual to the Schwartz space *is* the space of distributions

>> No.9775462
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9775462

>>9774509
>Who cares about what tails we have?
Literally anyone doing Fourier theory or PDE on non-compact sets. Namely anyone not fucking retarded, unlike you.
>>9774535
No, that's the space of [math]tempered[/math] distributions. Distributions are dual to conpactly supported smooth functions, not Schwarz functions.

>Schwartz
>>9774526
>Distrubtions are defined in function spaces
Jesus Christ LMAO imagine the amount of Dunning-Kruger required to make these posts. Embarrassing.