1:15 If we can't measure distances, so it is of zero point to depict a manifold as an encircled area. No linear measure, hence no areal measure. In such case, all elements of the manifold should take place in a single dot, idk how, though.
Just because you cannot define a distance doesn't mean you can't tell two points apart. A topological space generalizes some of the concepts we can define on the reals such as convergence, openness and closeness of sets, etc. and applies it to some larger class of sets
I would prefer if you made videos of new material rather than videos with the exact same material as you've already done except with another background color.
![Manifolds 4 | Quotient Spaces [dark version]](http://i.ytimg.com/vi/sXdQg1on3J4/mqdefault.jpg)
![Manifolds 4 | Quotient Spaces [dark version]](/img/tr.png)
This class is amazingly well made! I'm surprised with how I understand everything so easily, thank you so much!
You're very welcome!
Excellent presentation thank you!
What if you had an open set that only contained a? Then N would have to be infinity, and there would only be a finite number of elements, namely a.
N has to be a natural number, not infinity :)
Cheers for the new video😁
Cheers :)
1:16 I guess the notion of "metric" was an overkill in the genesis of mathematics.
1:15 Can't I just find a deference between the elements of the set to estimate the metric?
How would you define such a "difference" for abstract sets? (Assuming that is what you meant)
1:15 If we can't measure distances, so it is of zero point to depict a manifold as an encircled area. No linear measure, hence no areal measure. In such case, all elements of the manifold should take place in a single dot, idk how, though.
Just because you cannot define a distance doesn't mean you can't tell two points apart. A topological space generalizes some of the concepts we can define on the reals such as convergence, openness and closeness of sets, etc. and applies it to some larger class of sets
I would prefer if you made videos of new material rather than videos with the exact same material as you've already done except with another background color.
The good thing is: I do both :)
@@brightsideofmaths “Dark mode” for somewhat advanced math videos is incredible, hilarious and fantastic. Thank you!
@@rao_v Thanks :D
I think he is also ensuring accessibility of his videos by using different backgrounds. I would appreciate such an effort.