3 - Open and closed sets

This video continues the series, discussing open and closed sets, interiors and closure, and dense sets and separability of metric spaces. It follows the seventh page of my course handouts, corresponding to Chapter 4 in Carothers.

This video moves quickly (and has a lot of content)! Please rewind, rewatch, and/or slow the playback speed as necessary---once the whole thing makes sense in real time, you're in pretty good shape with the basic concepts!

[Ibrahmoment]

THE best video on open sets and closed sets. Very informative and concise. I really wish you'd have also introduced "boundary" of a set, especially since it slightly aids in developing intuition for open and closed sets. With that, the video would have been truly complete.

[NewDeal]

This has to be the best video on Youtube devoted to the subject. Let me elaborate:

1) Production quality is great. Clear audio, distinct voice, no annoying accent or background noise. Animations and illustrations seem right at their place, which is often not the case with other slide based presentations.

2) Great insights and intuition. Instead of unleashing a somewhat usual formalized hellfire, you manage to convey the core motivation behind every idea. Most of the time after having a lecture I feel the need to clarify some concepts going to Stackexchange or Mathoverflow, yet with your videos I don't feel the need.

3) Unlike some popular mathbloggers you don't stop at bare intuition, but go all the way, providing all the formal statements and derivations in a way that enhances understanding, not drowning it in symbolic nightmare. That's how true education (and not just science realted entertainment) should be done.

Do you have any plans for further videos? Perhaps some measure theory, global topology, even integration theory or differential equations? I admire you talent and approach. Well, I'd gladly pay for such content, hope you have Patreon or something?

Thanks again, that's exceptional!