Problem Set # 12
On the problem set, there are 3 points per problem. You have to have it all right to get all 3 points. A little tiny bit wrong and you get 2 points. A little bit right and you get 1 point. All wrong is 0.
Okay, this week I have two files from pages of Munkres.
and
These files serve several purposes. The purpose that inspired this is the proof that you cannot comb the hair on a ball. That proof is in the vector fields file. The first page tells you what a vector field is (hair on the ball) and the second and third pages give a proof. The theorem that there is no nonvanishing tangent vector field on S^2 is the cannot-comb-the-hair-on-a-ball theorem. It is a bit hard to see, which is why I give you the file to contemplate rather than me trying to draw pictures of it in class. But, the proof isn't really that hard for us now.
The next purpose is that in Problems From Munkres file, your homework is problem 5(a-d) and problem 7.