Topological Spaces Visually Explained

[@AbideByReason]

Hope you like the animations here. This is the first video I made using Manim. Huge thank you to Grant Sanderson (3blue1brown) and the community of developers who work on the open source project.

[@benjamingoldstein1111]

Well done! Manim works great for you!

[@Higgsinophysics]

Man these topologi animations are satisfying 😄 loved yhe vide o

[@speedcubesolver1195]

Great topic with beautiful animations! 💛💛👍

[@kristianwichmann9996]

I know the indiscrete topology as the "diffuse topology". Which is appropriate for a space where any sequence converges to any point.

[@kantamana1]

This is the truth about what topology is!

[@samylahlou]

Very interesting and clear video ! However, I have to say that I was expecting more visuals since the title is literally "Topological Spaces Visually Explained". It was very promising at first since you displayed some clean 3D shapes in the beginning and I was hoping to rely more on these shapes to explain what a topology is. At the end, most of the visuals were used to write the definition of a topological space or to write in set notation power sets. What I am saying is that I honestly find the video very good, easy to follow and with an excellent quality but the title is a little bit misleading.

[@goldenboy.]

Where does the vector space fit in this hierarchy of spaces founded by the topological space?

[@AbideByReason]

It's not really in the hiearchy. It might be better to think of it as an "algebraic structure" as opposed to a "space" in the way I was using spaces in this video. Only when you equip the vector space with an inner product does it become part of the hierarchy.

[@GeoffryGifari]

from what I've read so far, topology seems to be the mathematical study of holes

[@speedcubesolver1195]

😂😂

[@kristianwichmann9996]

Not quite; that would be homotopy and homology.

[@Gordy-io8sb]

Mathematician here. Nope. Topology is the study of surfaces, particularly those that are preserved in specific ways under transformations, in a given number of dimensions. That's why the concepts of homeomorphisms, certain groups, homotopies, etc. are so important to the subject. If topology was the study of holes, then wouldn't it be PREDOMINANTLY ABOUT HOLES? It isn't, so it's not. Well, a "hole" is kind of ill-defined without the fundamental group, but that's not important. What is important, is that topology is much more diverse than just "holes". But please, guide us with your knowledge, oh enlightened one. Surely all of the topologists like Grothendieck, Poincaré and Klein were wrong, and you're right, right? As Kristian said, the "study" of "holes" is more in the territory of homology and homotopy theory. Not topology itself. Pick up a topology book, preferably Munkres', and tell me where it says anything like "topology is the study of holes".

[@Gordy-io8sb]

But if you, someone who doesn't know their stuff, wants to challenge me, someone who does -- go right ahead, buddy. Tell me what topology is about.

[@GeoffryGifari]

@Gordy-io8sb sounds like holes to me