Due date: Friday 12/5/14 for reading; Monday 12/8/14 for problems.
Last update made by D. Groisser Mon Dec 1 21:29 EST 2014
- C: Read the handout Sufficient Conditions for Paracompactness of Manifolds. Note:
(i) For the purposes of this handout, “Hausdorff” and “second countable” are not part of the definition of “manifold”; they are extra conditions that can be imposed on a manifold. (ii) Recall that in a topological manifold, the overlap-maps within an atlas are required only to be continuous, rather than smooth. Every smooth manifold is a topological manifold. Thus anything proven in this handout about topological manifolds is also true for smooth manifolds. (iii) In the 2012 class for which I originally wrote these notes, I did use the terminology “second countable”, so you’ll see several appearances of the phrase “has a countable basis of open sets” (which is what second-countable means). - A: Tu problems: none.
- B: Click here for non-book problems. Of these, hand in only 1, 2, and 3.