10-327/Register of Good Deeds

• 10-327/Kai Yang 997712756

1.Register for the solution to the first and second assignment. e.g. Here is what I will do: Once we get our HW1 from the TA, I will correct all the mistakes(if any) , scan the HW and put it here.

2.For lecture 3. Complete proof for the equality of three topologies generated by basis B. And solution to the four exercises.

3.For lecture 4. Some more illustration on Uniqueness of the product topology satisfying condition 1&2. Complete proof of the subspace topology is the unique topology satisfying condition 1&2. Proof for a couple of claims: The product topology on R_std and R_std is the standard topology on R^2 and subspace topology on Z as a subspace of Y which is a subspace of Z is the same as the subspace topology on Z as a subspace of X, where Y is a subspace of X.

4.Register for the solution to the 3rd and 4th assignment. Some extra problem (not to be handed in) for HW2.

5.Annotated a few lecture videos.

6.A few more solutions to questions about metric spaces with illustrations.