I'm doing something I hate to do. I hate writing too many subscripts. This is like the stupidest construction in the universe. It's amazing anything comes out of this. I'm not proving this because I' m getting tired of teaching commutative algebra.
Life is tough.
On Homework -This is a quiz on topology. You passed the one quiz. But I'll leave that as an exercise to anybody with the determination to actually do it. I'm going to leave the details to the masochistic reader. There are lots of technical details, all of which are disgusting.