26:23 Why is it permissible to use the metric definition of open sets here when topology is upstream (and also has its own definitions of closed and open sets) and we have not yet defined a metric? Or is that the arigour here, i.e that we are just using the metric topology a little offhandedly to demonstrate the connectedness intuition?
What he says at 3:40 is just amazing, at least to me. That you cannot intelligibly speak of "open" or "closed" sets withing the realm of set theory alone.
True, it is very interesting from a metamathematical and epistemological point of view: we study what we choose to study, and these choices induce new things we'd like to study :D
Hi, thanks for the video. I have a question : if all open sets are elements of tao, may I know if all the elements of tao are just the open sets? Thanks again
My cat understood everything as well as me.
Excellently explained, thanks!
I never knew about this intuition behind topological spaces, everything makes more sense now! Thanks a bunch! :)
You are an amazing teacher, literally the best on youtube.
Great set of videos!
It's such a pity that I find your video until today. Great thanks for your excellent work!
Oh my god. Topology makes sense. Why don't people teach it like this? I mean, rigour can come after you've understood what's actually happening.
26:23 Why is it permissible to use the metric definition of open sets here when topology is upstream (and also has its own definitions of closed and open sets) and we have not yet defined a metric? Or is that the arigour here, i.e that we are just using the metric topology a little offhandedly to demonstrate the connectedness intuition?
What he says at 3:40 is just amazing, at least to me. That you cannot intelligibly speak of "open" or "closed" sets withing the realm of set theory alone.
True, it is very interesting from a metamathematical and epistemological point of view: we study what we choose to study, and these choices induce new things we'd like to study :D
Thank you. This was very helpful.
Hi, thanks for the video. I have a question : if all open sets are elements of tao, may I know if all the elements of tao are just the open sets? Thanks again
How do you know so much? 🤔
Thank you so much! This really helps!
Thank you.
Thank you!
can you please send me the next video.
Could anyone tell me what the next video is?