This question was inspired by this "beautiful mind" question, where some one asks about the mathematical contents of some movie. I do not see how this other question is less opinion-based than the one I am posing. This post also did not motivate anyone to censor it...
I am giving a summer course on topology starting on January 6th. I am thinking about showing the Hitler Learns Topology meme on our first class, and maybe, showing again on the last class, or after the chapter on connectedness.
But I have some doubts on the mathematical contents of the video, and I would be really thankful if someone could clarify those to me.
OF COURSE, since the problem is NOT fully shown, I just hope someone can recognize the theory they are talking about and explain it to me.
What is the "null set" they are talking about?
Is this "null set" the topological space they are talking about? Or is it just the "clopen" set in question?
I understood that the clopen set in question is "the zero of the points in the null set". What is this set? And why is it clopen?
What is the "close points" Hitler refers to?
Edit: I have edited the question so as to make it absolutely mathematical.