Unformatted text preview: manifold? Is it connected? • Repeat the experiment, but this time cutting the M¨ obius band one third of the distance from one of the edges. 4. MTA 3.1-5: Compacti±cation of R n . 5. [Guillemin and Pollack, page 5, #3] Let M , N , and P be smooth manifolds and let f : M → N and g : N → P be smooth maps. (a) Show that the composite map g ◦ f : M → P is smooth. (b) Show that if f and g are di²eomorphisms, so is g ◦ f . (You may use the fact that the composition of smooth functions between open subsets of Euclidian spaces are smooth.) 6. MTA 3.3-1: Graphs of manifolds...
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- Fall '08
- Derivative, Manifold, Smooth function, California Institute of Technology, M¨bius band