Manifolds

This video will look at the idea of a manifold and how it is formally defined. It will also provide an example of a change of coordinates as a mapping between open sets.

[sanjursan]

Nice to find all those arcane definitions clearly defined and in one compact space, er, easy to access place.

[ronbackal]

Great video! I saw those definitions in books and had a rough time trying to figure out what they meant. This video clearly clarifies those definitions

[mueezadam]

I accidentally left auto-generated subtitles on and had a brief moment of terror when I saw unfamiliar terms like “York Lydian space” appearing off the bat in an introductory lesson for a branch of mathematics I thought I was already somewhat acquainted with.

Anyway, great lesson!

[shihaowang]

Nice video and does make it clear for beginners to get started on some abstract topological knowledge. One suggestion, it would be great if simple examples or visualizations can be showed when a new concept is to be introduced, such as cover and refinement.

[Victoralencar]

Awesome video, man!
Thanks for made it

[zwitter]

This is quite good, especially when Robert is speaking; the silences between slides are too long and distracting. That may be due ot the vagaries of SCRENCAST but nonetheless, Robert doessuch a good job explaining this stuff and so the breaks are unproductive. In spite of this criticism thank you it is useful

[frede]

Hey, I am just wondering, what's the difference between a diffeomorphism and a homeomorphism? I am reading Sean Carroll's "An introduction to general relativity: spacetime and geometry", and he almost gives the exact same definition of a diffeomorphism as you give for a homeomorphism.

[tpvdwc]

Thank you, Robert, very helpful. Although, @6:39 you claim to give a formal definition of a manifold, but what you actually do is giving a definition of a *topological* manifold. Or is a topological manifold the same as an ordinary manifold?

[georgeveropoulos]

nice !! you have some application of manifold in physics ??

[alexsiryj]

I think you made a mistake at 1:21 when you defined a Hausdorff space. It should be if u and v are in T and u≠v, then there exist open neighbourhoods U and V such that U and V are disjoint. Otherwise we can clearly find contradictions to your definition with an example like the open sets (0, 2) (1, 3) being neighbourhoods of 1 and 2 with nonempty intersections.

[williamky]

Thank you, it’s a pretty good explanation

[shicongnie]

Awesome series! May you share the pdfs?

[macmos]

On the example, North Pole isn't projected because it cannot-- its projection is parallel to the plane, correct?

[manologodino]

Thank you for reading out loud the slides, nice summary but for a YouTube video I was expecting more explanation and less reading, like I had at the University. The slides are great though.

[achiltsompanos]

What the hell is a topological spice/speyce? Lol