The Separation Axioms (A Topology Visual)

A topology on a set gives a notion of "shape" or "vicinity" (loosely speaking) to the set. There are different classes of topological spaces based on how finely the topology can distinguish between two distinct points or sets in the space.

Here we provide a visual of five levels of this distinguishability: Kolmogorov (T0), Frechet (T1), Hausdorff (T2), Regular Hausdorff (T3), and Normal Hausdorff (T4).

(as well as previews, behind-the-scenes, and more content).

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[alkankondo]

For Axiom T-3 (Regular Hausdorff), shouldn't you also specify that the point CANNOT be contained by the closed set? Isn't it possible to have a point contained in a closed set where it is IMPOSSIBLE to form an open set around the point that is disjoint from the closed set, right? (Especially if the point is an isolated point, this isn't possible.)

[MathManMcGreal]

Was I just initiated into a topology cult???

[cosmicentitynahtnj]

_If you gaze for long into an abyss, _

_the abyss gazes also into you._

[stydras]

Boi, that's some nice editing. Nice to see some "advanced" pure mathematics video thats not boring

[Rien--]

this is what i'd imagine life looks like on DMT.


sick editing btw

[enochsadventures]

most people: math is not cool
me: **showing them this video**
most people: math is not cool
me: I thought it was :(

[gz]

... This is just too much. I feel the power of the sets!

[cosmicentitynahtnj]

_I grant to you a soldier who has no heart._

_One who shall not falter in the darkness._

[dudewaldo]

This was lit as hell can this guy teach an entire topology course

[Topples]

I never thought I would learn topology from Skeletor, but here we are.

[ezekielschmittart]

Math, magick, and tool? How did i not find this channel sooner

[samhollins]

*this is now a Tool music video channel.*

[bramlentjes]

Nice video and awesome graphics! What about T_{2.5} and T_{3.5}?

[gog_magpie]

I am glad that I'm subbed to this channel

[TASPlasma]

Any plans on making this but for Grothendieck's axioms and the axioms for an abelian category?

[peterosudar]

The real analysis class, that caused me an actual existential crisis, is trying to make a come back through this video.


If you like this comment then you are adding to my actual existential crisis, in reality.

Thank you in advance.

Seriously.

[haminatmiyaxwen]

"Prison Topology" by Epic Math Time. Awesome video and of course the music makes it that much better 😂

[nostalgia_]

Awesome, can you have the dude with the sceptre teach us low dimensional topology also?

[chin]

Somewhat of a late comment, but for T3 and T4, shouldn't the topology satisfy the listed properties AND also be T1? Like there's no guarantee that a singleton is a closed set without assumptions of T1, so T3 and T4 does not end up being stronger than T2. I know some authors define Regular and Normal without the assumptions of T1, but you even wrote Regular Hausdorff and Normal Hausdorff. Just pointing this out. Great video, tho!

[angrycat]

sick video. You deserve x10 more subs.