Thanks for the corrections, I'll get on that.
I was having a similar idea actually, I was thinking that around exam time I would ask for sample questions, mostly things that people are struggling on or have seen in a practise paper and try and whizz through a bunch of them on video. Now that you mention it though, it might be a way cooler to take a load of sample questions, (some from students, and some just plain evil ones) and just write them out on video, let the comments frenzy over them for a week, and then write out the solutions on video a week later. That could be a lot of fun!
Your idea touches on another distant idea I had. I recently picked up the book Topological Groups and Related Structures by Alexander Arhangel'skii, which is a quite recent expository on basically everything we know about Topological Algebra (it's huge), and in there are hundreds and hundreds of bitesized open problems, small enough to explain in 510 minutes and many are very interesting. Now obviously I haven't covered even remotely enough material for the expected audience to understand them, but I figured that once I had I could just throw out one a week, talk a little about it, and see if the combined viewer base could have a genuine crack at it!
Also, I'd like your opinion on the best order to go through limit points and closure. My next three videos are gonna cover neighbourhood basis and then countability axioms but not separability, and then I would cover separability at the same time as density. First I figured since I already defined closed sets abstractly I could just go right ahead with the intersection of all closed sets approach, but then how do you link it back to limit points without it seeming forced? Should I instead start at sequences in metric spaces? Might take forever, and I don't want to revisit metric spaces too heavily. Maybe I could just talk about nets first. It just seems any way I try to order it some rigor is sacrificed. Where do you think is the best place to start?
